{"id":297318,"date":"2023-12-25T16:24:44","date_gmt":"2023-12-25T09:24:44","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=297318"},"modified":"2023-12-25T16:24:44","modified_gmt":"2023-12-25T09:24:44","slug":"cong-thuc-to-hop-chinh-hop","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/","title":{"rendered":"B\u1ed9 c\u00f4ng th\u1ee9c Ho\u00e1n v\u1ecb &#8211; Ch\u1ec9nh h\u1ee3p &#8211; T\u1ed5 h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t trong To\u00e1n h\u1ecdc"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">B\u1ed9 c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb lu\u00f4n khi\u1ebfn c\u00e1c b\u1ea1n h\u1ecdc sinh THPT d\u1ec5 nh\u1ea7m l\u1eabn gi\u1eefa c\u00e1c \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u00ednh x\u00e1c. Trong qu\u00e1 tr\u00ecnh h\u1ecdc th\u00ec c\u00e1c b\u1ea1n ph\u1ea3i ph\u00e2n bi\u1ec7t r\u00f5 ba lo\u1ea1i c\u00f4ng th\u1ee9c n\u00e0y th\u00ec m\u1edbi l\u00e0m b\u00e0i t\u1eadp v\u00e0 b\u00e0i thi hi\u1ec7u qu\u1ea3. B\u00e0i vi\u1ebft sau s\u1ebd gi\u1edbi thi\u1ec7u r\u00f5 h\u01a1n v\u1ec1 c\u00f4ng th\u1ee9c ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, ho\u00e1n v\u1ecb cho c\u00e1c b\u1ea1n t\u00ecm hi\u1ec3u th\u1eadt chu\u1ea9n.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Ho\u00e1n v\u1ecb trong to\u00e1n h\u1ecdc v\u00e0 c\u00e1c d\u1ea1ng th\u01b0\u1eddng g\u1eb7p<\/span><\/h2>\n<p>\u0110\u1ea7u ti\u00ean ch\u00fang ta s\u1ebd t\u00ecm hi\u1ec3u v\u1ec1 ho\u00e1n v\u1ecb v\u00e0 nh\u1eefng ki\u1ec3u ho\u00e1n v\u1ecb hay g\u1eb7p nh\u1ea5t:<\/p>\n<h3><span style=\"font-weight: 400;\">\u0110\u1ecbnh ngh\u0129a ho\u00e1n v\u1ecb<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">N\u1ebfu gi\u1ea3i th\u00edch m\u1ed7i t\u1eeb th\u00ec c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 coi t\u1eeb &#8220;ho\u00e1n&#8221; c\u00f3 ngh\u0129a l\u00e0 &#8220;ho\u00e1n \u0111\u1ed5i&#8221; v\u00e0 t\u1eeb &#8220;v\u1ecb&#8221; c\u00f3 ngh\u0129a l\u00e0 &#8220;v\u1ecb tr\u00ed&#8221;. Ch\u1eb3ng h\u1ea1n ch\u00fang ta c\u00f3 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 X bao g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed kh\u00e1c nhau (\u0111i\u1ec1u ki\u1ec7n l\u00e0 n \u2265 0). Nh\u01b0 v\u1eady th\u00ec t\u1eebng ki\u1ec3u s\u1eafp x\u1ebfp c\u00e1c ph\u1ea7n t\u1eed thu\u1ed9c t\u1eadp h\u1ee3p X theo m\u1ed9t th\u1ee9 t\u1ef1 c\u1ee5 th\u1ec3 \u0111\u01b0\u1ee3c coi l\u00e0 1 ho\u00e1n v\u1ecb c\u1ee7a \u201cn\u201d. Th\u01b0\u1eddng th\u00ec s\u1ed1 l\u01b0\u1ee3ng ho\u00e1n v\u1ecb c\u1ee7a \u201cn\u201d s\u1ebd \u0111\u01b0\u1ee3c vi\u1ebft k\u00fd hi\u1ec7u ng\u1eafn g\u1ecdn l\u00e0 \u201cPn\u201d.<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-297322 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-1.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3><span style=\"font-weight: 400;\">Ho\u00e1n v\u1ecb c\u00f3 m\u1ea5y d\u1ea1ng th\u01b0\u1eddng g\u1eb7p?<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Hi\u1ec7n nay c\u00f3 3 lo\u1ea1i th\u01b0\u1eddng g\u1eb7p \u0111\u00f3 l\u00e0:<\/span><\/p>\n<h4><span style=\"font-weight: 400;\">Ho\u00e1n v\u1ecb d\u1ea1ng l\u1eb7p<\/span><\/h4>\n<p><span style=\"font-weight: 400;\">\u0110\u00e2y l\u00e0 d\u1ea1ng ho\u00e1n v\u1ecb m\u00e0 khi ch\u00fang ta cho s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d \u0111\u1ed1i t\u01b0\u1ee3ng v\u00e0 trong s\u1ed1 \u0111\u1ed1i t\u01b0\u1ee3ng \u0111\u00f3 c\u00f3 \u201cni\u201d c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng thu\u1ed9c lo\u1ea1i \u201ci\u201d \u0111\u1ed3ng th\u1eddi c\u00f3 nh\u1eefng ki\u1ec3u c\u1ea5u tr\u00fac y h\u1ec7t nhau. Hi\u1ec3u \u0111\u01a1n gi\u1ea3n th\u00ec v\u1edbi t\u1eebng ki\u1ec3u s\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 n ph\u1ea7n t\u1eed th\u00ec trong \u0111\u00f3 s\u1ebd c\u00f3 kho\u1ea3ng \u201cn1\u201d ph\u1ea7n t\u1eed s\u1ebd l\u00e0 \u201ca1, n2\u201d ph\u1ea7n t\u1eed s\u1ebd l\u00e0 \u201ca2\u201d\u2026 v\u00e0 c\u00f3 \u201cnk\u201d ph\u1ea7n t\u1eed s\u1ebd l\u00e0 \u201cak\u201d (n1 + n2 + n3 +&#8230;..+ nk = n) \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 ng\u1eabu nhi\u00ean v\u00e0 \u0111\u00f3 \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ed9t ho\u00e1n v\u1ecb d\u1ea1ng l\u1eb7p c\u00f3 c\u1ea5p l\u00e0 \u201cn\u201d v\u1edbi ki\u1ec3u (n1, n2,&#8230;, nk) thu\u1ed9c \u201ck\u201d ph\u1ea7n t\u1eed.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eebng ki\u1ec3u s\u1eafp x\u1ebfp bao g\u1ed3m th\u1ee9 t\u1ef1 l\u00e0 \u201cn\u201d ph\u1ea7n t\u1eed \u0111\u00e3 cho th\u00ec \u0111\u00f3 g\u1ecdi l\u00e0 1 ho\u00e1n v\u1ecb d\u1ea1ng l\u1eb7p thu\u1ed9c \u201cn\u201d.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n lo\u1ea1i ho\u00e1n v\u1ecb d\u1ea1ng l\u1eb7p s\u1ebd l\u00e0:<\/span><\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-297931 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-20\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3, ta c\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u201cPn\u201d l\u00e0 ho\u00e1n v\u1ecb d\u1ea1ng l\u1eb7p c\u00f3 c\u1ea5p \u201cn\u201d v\u1edbi ki\u1ec3u (n1,n2,&#8230;, nk) c\u1ee7a s\u1ed1 l\u01b0\u1ee3ng \u201ck\u201d ph\u1ea7n t\u1eed.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">n = n1 + n2 +&#8230;..+ nk: S\u1ed1 ph\u1ea7n t\u1eed.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u201cn1\u201d l\u00e0 s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed \u201ca1\u201d c\u00f3 c\u1ea5u tr\u00fac gi\u1ed1ng nhau<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u201cn2\u201d l\u00e0 s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed \u201ca2\u201d c\u00f3 c\u1ea5u tr\u00fac gi\u1ed1ng nhau.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u201cnk\u201d l\u00e0 s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed \u201cak\u201d c\u00f3 c\u1ea5u tr\u00fac gi\u1ed1ng nhau.<\/span><\/li>\n<\/ul>\n<h4><span style=\"font-weight: 400;\">Ho\u00e1n v\u1ecb d\u1ea1ng v\u00f2ng<\/span><\/h4>\n<p><span style=\"font-weight: 400;\">\u0110\u00e2y l\u00e0 d\u1ea1ng ho\u00e1n v\u1ecb bao g\u1ed3m nh\u1eefng ph\u1ea7n t\u1eed \u1edf b\u00ean trong c\u1ee7a ho\u00e1n v\u1ecb c\u00f3 th\u1ec3 t\u1ea1o ra 1 v\u00f2ng c\u00f9ng v\u1edbi s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed l\u00e0 k l\u1edbn h\u01a1n 1 v\u00e0 \u201ck\u201d ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean. C\u00f4ng th\u1ee9c t\u00ednh ho\u00e1n v\u1ecb\u00a0 d\u1ea1ng v\u00f2ng l\u00e0: <\/span><\/p>\n<p style=\"text-align: center;\"><strong>Q(n) = (n-1)!<\/strong><\/p>\n<h4><span style=\"font-weight: 400;\">Ho\u00e1n v\u1ecb d\u1ea1ng \u0111\u1ed3ng nh\u1ea5t<\/span><\/h4>\n<p><span style=\"font-weight: 400;\">Hay nhi\u1ec1u ng\u01b0\u1eddi c\u00f2n g\u1ecdi l\u00e0 ho\u00e1n v\u1ecb \u0111\u1ed5i ch\u1ed7, \u0111\u00e2y l\u00e0 ki\u1ec3u ho\u00e1n v\u1ecb c\u00f3 ph\u1ea7n t\u1eed \u0111\u1ea7u ti\u00ean v\u1edbi ph\u1ea7n t\u1eed \u0111\u1ea7u ti\u00ean, ph\u1ea7n t\u1eed 2 v\u1edbi ph\u1ea7n t\u1eed 2\u2026 Ngh\u0129a l\u00e0 th\u1ef1c t\u1ebf th\u00ec kh\u00f4ng c\u00f3 s\u1ef1 \u0111\u1ed5i ch\u1ed7 gi\u1eefa nh\u1eefng ph\u1ea7n t\u1eed n\u00e0y.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">T\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p l\u00e0 g\u00ec?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p th\u00ec m\u1ecdi ng\u01b0\u1eddi ph\u1ea3i t\u00ecm hi\u1ec3u kh\u00e1i ni\u1ec7m sau \u0111\u00e2y:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">\u0110\u1ecbnh ngh\u0129a t\u1ed5 h\u1ee3p<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">T\u1ed5 h\u1ee3p l\u00e0 ph\u01b0\u01a1ng ph\u00e1p m\u00e0 ch\u00fang ta ch\u1ecdn c\u00e1c ph\u1ea7n t\u1eed trong nh\u00f3m l\u1edbn m\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i ph\u00e2n bi\u1ec7t v\u1ec1 m\u1eb7t s\u1eafp x\u1ebfp th\u1ee9 t\u1ef1. \u1ede m\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p th\u00ec c\u00e1c b\u1ea1n \u0111\u01b0\u1ee3c \u0111\u1ebfm c\u1ea3 s\u1ed1 l\u01b0\u1ee3ng t\u1ed5 h\u1ee3p. T\u1ed5 h\u1ee3p c\u00f3 d\u1ea1ng ch\u1eadp \u201ck\u201d c\u1ee7a s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed ngh\u0129a l\u00e0 s\u1ed1 c\u00e1c nh\u00f3m bao g\u1ed3m \u201ck\u201d ph\u1ea7n t\u1eed l\u1ea5y ra t\u1eeb nh\u00f3m \u201cn\u201d ph\u1ea7n t\u1eed v\u00e0 gi\u1eefa n\u00f3 ch\u1ec9 c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t v\u1ec1 nh\u1eefng th\u00e0nh ph\u1ea7n trong c\u1ea5u tr\u00fac ch\u1ee9 ch\u01b0a xem x\u00e9t th\u1ee9 t\u1ef1 c\u1ee7a nh\u1eefng ph\u1ea7n t\u1eed.<\/span><\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-299179 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20-1.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-20\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-20-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">V\u1edbi t\u1eebng t\u1eadp h\u1ee3p con bao g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201ck\u201d ph\u1ea7n t\u1eed trong t\u1eadp h\u1ee3p l\u1edbn bao g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed (v\u1edbi n&gt;0) th\u00ec \u0111\u01b0\u1ee3c coi l\u00e0 t\u1ed5 h\u1ee3p g\u1ed3m ch\u1eadp \u201ck\u201d c\u1ee7a s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">\u0110\u1ecbnh ngh\u0129a ch\u1ec9nh h\u1ee3p<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u00e2y l\u00e0 ph\u01b0\u01a1ng ph\u00e1p m\u00e0 ch\u00fang ta ch\u1ecdn c\u00e1c ph\u1ea7n t\u1eed trong 1 t\u1eadp h\u1ee3p l\u1edbn h\u01a1n m\u00e0 v\u1eabn ph\u00e2n bi\u1ec7t v\u1ec1 th\u1ee9 t\u1ef1 s\u1eafp x\u1ebfp. \u0110i\u1ec1u n\u00e0y ng\u01b0\u1ee3c l\u1ea1i v\u1edbi d\u1ea1ng t\u1ed5 h\u1ee3p l\u00e0 n\u00f3 kh\u00f4ng c\u1ea7n s\u1ef1 ph\u00e2n bi\u1ec7t v\u1ec1 m\u1eb7t th\u1ee9 t\u1ef1.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299180 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-21.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-21\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-21.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-21-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-21-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 ch\u1ec9nh h\u1ee3p g\u1ed3m ch\u1eadp \u201ck\u201d c\u1ee7a \u201cn&#8221; s\u1ebd l\u00e0 1 t\u1eadp h\u1ee3p con c\u1ee7a 1 t\u1eadp h\u1ee3p l\u1edbn S bao g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed. T\u1eadp h\u1ee3p con n\u00e0y s\u1ebd bao g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201ck\u201d ph\u1ea7n t\u1eed thu\u1ed9c t\u1eadp S v\u00e0 tu\u00e2n theo m\u1ed9t th\u1ee9 t\u1ef1 s\u1eafp x\u1ebfp.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">B\u1ed9 c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t k\u00e8m v\u00ed d\u1ee5\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau \u0111\u00e2y l\u00e0 b\u1ed9 c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t trong To\u00e1n h\u1ecdc:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u1ec9nh h\u1ee3p<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Theo kh\u00e1i ni\u1ec7m \u0111\u1ec1 c\u1eadp \u1edf tr\u00ean th\u00ec ch\u00fang ta c\u00f3 s\u1ed1 l\u01b0\u1ee3ng ch\u1ec9nh h\u1ee3p ch\u1eadp \u201ck\u201d c\u1ee7a 1 t\u1eadp h\u1ee3p bao g\u1ed3m \u201cn\u201d ph\u1ea7n t\u1eed (1\u2264 k \u2264 n) s\u1ebd \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c:<\/span><\/p>\n<figure id=\"attachment_297325\" aria-describedby=\"caption-attachment-297325\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297325\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-4.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-297325\" class=\"wp-caption-text\">C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u1ec9nh h\u1ee3p<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda 1: Ch\u00fang ta c\u00f3 m\u1ea5y c\u00e1ch s\u1eafp x\u1ebfp 3 b\u1ea1n Ho\u00e0ng, Hi\u1ebfu, H\u01b0ng v\u00e0o 2 ch\u1ed7 ng\u1ed3i \u0111\u00e3 c\u00f3 s\u1eb5n?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297326 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-5.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda 2: C\u00f3 m\u1ea5y s\u1ed1 bao g\u1ed3m 04 ch\u1eef s\u1ed1 ho\u00e0n to\u00e0n kh\u00e1c \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp t\u1eeb nh\u1eefng ch\u1eef s\u1ed1 l\u00e0 1,2,3,4,5,6,7.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ch\u00fang ta s\u1ebd c\u00f3 t\u1eebng s\u1ed1 bao g\u1ed3m b\u1ed1n ch\u1eef s\u1ed1 ho\u00e0n to\u00e0n kh\u00e1c \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp t\u1eeb vi\u1ec7c l\u1ea5y ra 04 ch\u1eef s\u1ed1 c\u1ee7a t\u1eadp h\u1ee3p A g\u1ed3m c\u00e1c ph\u1ea7n t\u1eed l\u00e0 1, 2, 3, 4, 5, 6, 7 r\u1ed3i s\u1eafp x\u1ebfp n\u00f3 theo nh\u1eefng th\u1ee9 t\u1ef1 c\u1ee5 th\u1ec3. T\u1eebng s\u1ed1 n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c xem l\u00e0 1 ch\u1ec9nh h\u1ee3p c\u00f3 ch\u1eadp 04 c\u1ee7a 07 ph\u1ea7n t\u1eed.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Suy ra s\u1ed1 l\u01b0\u1ee3ng s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u01b0\u1ee3c t\u1ea1o ra t\u1eeb t\u1eadp h\u1ee3p tr\u00ean l\u00e0 840 s\u1ed1.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n t\u1ed5 h\u1ee3p<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Khi nh\u1eafc \u0111\u1ebfn c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ch\u00fang ta s\u1ebd c\u00f3 c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5 h\u1ee3p g\u1ed3m ch\u1eadp \u201ck\u201d c\u1ee7a s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed (1\u2264 k \u2264 n) l\u00e0:<\/span><\/p>\n<figure id=\"attachment_297327\" aria-describedby=\"caption-attachment-297327\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297327\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-6.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-297327\" class=\"wp-caption-text\">C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n t\u1ed5 h\u1ee3p<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3 \u201ckn\u201d c\u00f3 \u0111\u00e1p \u00e1n l\u00e0 0 khi k &gt; n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda: \u00d4ng B c\u00f3 ch\u01a1i v\u1edbi t\u1ed5ng c\u1ed9ng 11 ng\u01b0\u1eddi. Nh\u01b0ng \u00f4ng B mu\u1ed1n g\u1eedi l\u1eddi m\u1eddi cho 05 ng\u01b0\u1eddi trong s\u1ed1 h\u1ecd \u0111i \u0103n c\u00f9ng. Trong s\u1ed1 11 ng\u01b0\u1eddi b\u1ea1n \u0111\u00f3 th\u00ec c\u00f3 02 ng\u01b0\u1eddi l\u00e0 kh\u00f4ng mu\u1ed1n \u0111i g\u1eb7p m\u1eb7t. V\u1eady \u00f4ng B s\u1ebd c\u00f3 m\u1ea5y c\u00e1ch \u0111\u1ec3 m\u1eddi h\u1ecd \u0111i \u0103n?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00d4ng B ch\u1ec9 c\u00f3 th\u1ec3 m\u1eddi m\u1ed9t trong hai ng\u01b0\u1eddi b\u1ea1n v\u00e0 \u00f4ng s\u1ebd m\u1eddi th\u00eam kho\u1ea3ng 4 ng\u01b0\u1eddi b\u1ea1n trong 9 ng\u01b0\u1eddi b\u1ea1n kia. Nh\u01b0 v\u1eady ta c\u00f3:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297328 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-7.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">\u00d4ng B kh\u00f4ng g\u1eedi l\u1eddi m\u1eddi cho hai ng\u01b0\u1eddi b\u1ea1n kia m\u00e0 ch\u1ec9 g\u1eedi l\u1eddi m\u1eddi cho 5 ng\u01b0\u1eddi trong ch\u00edn ng\u01b0\u1eddi b\u1ea1n. Nh\u01b0 v\u1eady ta c\u00f3:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297329 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-8.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">T\u1ed5ng c\u1ed9ng l\u00e0 \u00f4ng B s\u1ebd c\u00f3 328 c\u00e1ch \u0111\u1ec3 m\u1eddi.\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ho\u00e1n v\u1ecb<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh to\u00e1n ho\u00e1n v\u1ecb kh\u00e1 \u0111\u01a1n gi\u1ea3n. N\u1ebfu ch\u00fang ta c\u00f3 m\u1ed9t t\u1eadp h\u1ee3p bao g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed (\u0111i\u1ec1u ki\u1ec7n n&gt; 0) th\u00ec ta c\u00f3 c\u00f4ng th\u1ee9c t\u00ednh ho\u00e1n v\u1ecb c\u1ee7a s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed nh\u01b0 d\u01b0\u1edbi \u0111\u00e2y:<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Pn=n!\u00a0<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299181 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-22.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-22\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-22.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-22-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-22-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp minh h\u1ecda 1: Cho 1 t\u1eadp h\u1ee3p t\u00ean l\u00e0 A g\u1ed3m 5 s\u1ed1 l\u00e0 3, 4, 5, 6, 7. D\u1ef1a tr\u00ean t\u1eadp h\u1ee3p n\u00e0y th\u00ec c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp \u0111\u01b0\u1ee3c m\u1ea5y s\u1ed1 t\u1ef1 nhi\u00ean bao g\u1ed3m 5 ch\u1eef s\u1ed1 kh\u00e1c nhau?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n: B\u1ea1n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh ho\u00e1n v\u1ecb l\u00e0 Pn=n!. Nh\u01b0 v\u1eady ta c\u00f3 P5 = 5! v\u00e0 \u0111\u00e1p \u00e1n l\u00e0 120 s\u1ed1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp minh h\u1ecda 2: C\u00e1c b\u1ea1n h\u00e3y t\u00ednh to\u00e1n s\u1ed1 ki\u1ec3u s\u1eafp x\u1ebfp cho 10 b\u1ea1n th\u00e0nh 1 h\u00e0ng theo chi\u1ec1u d\u1ecdc?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eebng ki\u1ec3u s\u1eafp x\u1ebfp cho 10 b\u1ea1n th\u00e0nh 1 h\u00e0ng theo chi\u1ec1u d\u1ecdc ch\u00ednh l\u00e0 m\u1ed9t ki\u1ec3u ho\u00e1n v\u1ecb c\u1ee7a 10 ph\u1ea7n t\u1eed. Nh\u01b0 v\u1eady, s\u1ed1 ki\u1ec3u s\u1eafp x\u1ebfp 10 b\u1ea1n th\u00e0nh 1 h\u00e0ng d\u1ecdc \u0111\u00f3 l\u00e0 P10 = 10!<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ed1i quan h\u1ec7 c\u1ee7a ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, ho\u00e1n v\u1ecb trong to\u00e1n h\u1ecdc<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Qua kh\u00e1i ni\u1ec7m v\u00e0 nh\u1eefng c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb \u1edf tr\u00ean th\u00ec ch\u00fang ta c\u00f3 th\u1ec3 th\u1ea5y n\u00f3 c\u00f3 m\u1ed1i quan h\u1ec7 ch\u1eb7t ch\u1ebd v\u1edbi nhau. C\u1ee5 th\u1ec3 l\u00e0 1 ch\u1ec9nh h\u1ee3p c\u00f3 ch\u1eadp \u201ck\u201d c\u1ee7a \u201cn\u201d ph\u1ea7n t\u1eed s\u1ebd \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp b\u1eb1ng vi\u1ec7c ti\u1ebfn h\u00e0nh hai b\u01b0\u1edbc sau:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 1: B\u1ea1n l\u1ea5y m\u1ed9t t\u1ed5 h\u1ee3p c\u00f3 ch\u1eadp \u201ck\u201d c\u1ee7a \u201cn\u201d ph\u1ea7n t\u1eed.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 2: B\u1ea1n th\u1ef1c hi\u1ec7n ho\u00e1n v\u1ecb cho \u201ck\u201d ph\u1ea7n t\u1eed.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">V\u00ec v\u1eady m\u00e0 c\u00e1c b\u1ea1n s\u1ebd c\u00f3 c\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 th\u1ec3 hi\u1ec7n m\u1ed1i quan h\u1ec7 gi\u1eefa t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p v\u00e0 ho\u00e1n v\u1ecb nh\u01b0 sau:<\/span><\/p>\n<figure id=\"attachment_297331\" aria-describedby=\"caption-attachment-297331\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-297331\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-10.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-297331\" class=\"wp-caption-text\">C\u00f4ng th\u1ee9c th\u1ec3 hi\u1ec7n m\u1ed1i quan h\u1ec7 c\u1ee7a ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, ho\u00e1n v\u1ecb trong to\u00e1n h\u1ecdc<\/figcaption><\/figure>\n<h2><span style=\"font-weight: 400;\">Quy t\u1eafc \u0111\u1ebfm ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, ho\u00e1n v\u1ecb ch\u00ednh x\u00e1c<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p th\u00ec c\u00e1c b\u1ea1n h\u1ecdc sinh n\u00ean n\u1eafm th\u00eam c\u00e1c quy t\u1eafc \u0111\u1ebfm ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, ho\u00e1n v\u1ecb ch\u00ednh x\u00e1c nh\u01b0 sau:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Quy t\u1eafc d\u00f9ng \u0111\u1ec3 \u0111\u1ebfm c\u00e1c t\u1ed5 h\u1ee3p<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 1 t\u1eadp h\u1ee3p A g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng n ph\u1ea7n t\u1eed v\u1edbi \u0111i\u1ec1u ki\u1ec7n l\u00e0 n &gt; 0. Nh\u01b0 v\u1eady 1 t\u1ed5 h\u1ee3p ch\u1eadp \u201ck\u201d ng\u1eabu nhi\u00ean c\u1ee7a nh\u1eefng ph\u1ea7n t\u1eed thu\u1ed9c t\u1eadp A s\u1ebd l\u00e0 1 t\u1eadp con c\u00f3 kho\u1ea3ng \u201ck\u201d ph\u1ea7n t\u1eed thu\u1ed9c A, trong \u0111\u00f3 0 \u2a7d k \u2a7d n ; k <\/span><span style=\"font-weight: 400;\">\u2208 N.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady s\u1ed1 l\u01b0\u1ee3ng t\u1ed5 h\u1ee3p s\u1ebd \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n d\u1ef1a tr\u00ean c\u00f4ng th\u1ee9c n\u00e0y: n!(n-k)!<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Quy t\u1eafc d\u00f9ng \u0111\u1ec3 \u0111\u1ebfm c\u00e1c ch\u1ec9nh h\u1ee3p<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 1 t\u1eadp A g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed v\u1edbi n\u2a7e1. Nh\u01b0 v\u1eady 1 ch\u1ec9nh h\u1ee3p c\u00f3 ch\u1eadp \u201ck\u201d ph\u1ea7n t\u1eed ph\u00e2n bi\u1ec7t thu\u1ed9c A. Trong \u0111\u00f3 c\u00f3 1\u2a7dk\u2a7dn, k \u2208 N.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady s\u1ed1 l\u01b0\u1ee3ng ch\u1ec9nh h\u1ee3p \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n d\u1ef1a tr\u00ean c\u00f4ng th\u1ee9c n\u00e0y: n!k!(n-k)!<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299185 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-26.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-26\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-26.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-26-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-26-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3><span style=\"font-weight: 400;\">Quy t\u1eafc d\u00f9ng \u0111\u1ec3 \u0111\u1ebfm c\u00e1c ho\u00e1n v\u1ecb<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">V\u1edbi 1 t\u1eadp h\u1ee3p g\u1ed3m s\u1ed1 l\u01b0\u1ee3ng \u201cn\u201d ph\u1ea7n t\u1eed ph\u00e2n bi\u1ec7t th\u00ec ch\u00fang ta s\u1ebd l\u1eadp \u0111\u01b0\u1ee3c 1 ho\u00e1n v\u1ecb c\u1ee7a \u201cr\u201d ph\u1ea7n t\u1eed l\u1ea5y ra t\u1eeb t\u1eadp h\u1ee3p nh\u01b0 sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">L\u1ea5y ph\u1ea7n t\u1eed th\u1ee9 nh\u1ea5t th\u00ec ta s\u1ebd c\u00f3 t\u1ed5ng n c\u00e1ch;<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">L\u1ea5y ph\u1ea7n t\u1eed th\u1ee9 2 th\u00ec ta s\u1ebd c\u00f3 n-1 ki\u1ec3u s\u1eafp x\u1ebfp ho\u00e1n v\u1ecb;<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u2026.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">T\u01b0\u01a1ng t\u1ef1 khi ta l\u1ea5y ph\u1ea7n t\u1eed th\u1ee9 r trong t\u1eadp h\u1ee3p th\u00ec ta c\u00f3 r-1 ki\u1ec3u s\u1eafp x\u1ebfp ho\u00e1n v\u1ecb:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tr\u01b0\u1eddng h\u1ee3p m\u00e0 r = n th\u00ec ta s\u1ebd c\u00f3 c\u00f4ng th\u1ee9c \u0111\u1ebfm s\u1ed1 l\u01b0\u1ee3ng h\u00f3a v\u1ecb kh\u00e1c nhau \u0111\u01b0\u1ee3c l\u1eadp t\u1eeb n ph\u1ea7n t\u1eed. \u0110\u00f3 l\u00e0: P(n) = n!<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tr\u01b0\u1eddng h\u1ee3p m\u00e0 r &lt; n th\u00ec s\u1ed1 ho\u00e1n v\u1ecb s\u1ebd \u0111\u01b0\u1ee3c \u0111\u1ebfm theo c\u00f4ng th\u1ee9c n\u00e0y: P(n,r)= n!(n-r)!<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp minh h\u1ecda cho c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau khi n\u1eafm \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb th\u00ec c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 xem m\u1ed9t v\u00e0i b\u00e0i t\u1eadp minh h\u1ecda nh\u01b0 sau:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 1<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 thi m\u00f4n to\u00e1n c\u1ee7a l\u1edbp 12 \u1edf m\u1ed9t tr\u01b0\u1eddng THPT g\u1ed3m 2 lo\u1ea1i \u0111\u1ec1 tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn. T\u1eebng h\u1ecdc sinh khi d\u1ef1 thi ph\u1ea3i l\u00e0m 2 \u0111\u1ec1 thi bao g\u1ed3m 1 tr\u1eafc nghi\u1ec7m v\u00e0 1 t\u1ef1 lu\u1eadn. Trong \u0111\u00f3 c\u00f3 12 \u0111\u1ec1 t\u1ef1 lu\u1eadn v\u00e0 15 \u0111\u1ec1 tr\u1eafc nghi\u1ec7m. V\u1eady h\u1ecfi t\u1eebng h\u1ecdc sinh s\u1ebd c\u00f3 m\u1ea5y c\u00e1ch \u0111\u1ec3 ch\u1ecdn \u0111\u1ec3 thi?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3i:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta s\u1ebd c\u00f3 s\u1ed1 c\u00e1ch \u0111\u1ec3 ch\u1ecdn m\u1ed9t \u0111\u1ec1 t\u1ef1 lu\u1eadn l\u00e0: 12 c\u00e1ch v\u00e0 s\u1ed1 c\u00e1ch \u0111\u1ec3 ch\u1ecdn m\u1ed9t \u0111\u1ec1 tr\u1eafc nghi\u1ec7m s\u1ebd l\u00e0 15 c\u00e1ch. V\u00ec v\u1eady 1 b\u1ea1n h\u1ecdc sinh ph\u1ea3i th\u1ef1c hi\u1ec7n song song c\u1ea3 hai \u0111\u1ec1. Cho n\u00ean s\u1ebd c\u00f3 t\u1ea5t c\u1ea3 l\u00e0 12 x 15 = 180 c\u00e1ch \u0111\u1ec3 ch\u1ecdn \u0111\u1ec1 thi.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 2<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 m\u1ed9t t\u1eadp h\u1ee3p A bao g\u1ed3m c\u00e1c ch\u1eef s\u1ed1 l\u00e0 1, 2, 3, 5, 7, 9:<\/span><\/p>\n<p>a. T\u1eeb t\u1eadp h\u1ee3p tr\u00ean c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp \u0111\u01b0\u1ee3c m\u1ea5y s\u1ed1 t\u1ef1 nhi\u00ean bao g\u1ed3m 04 ch\u1eef s\u1ed1 t\u1eebng \u0111\u00f4i m\u1ed9t kh\u00e1c nhau.<\/p>\n<p>b. T\u1eeb t\u1eadp h\u1ee3p tr\u00ean c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp \u0111\u01b0\u1ee3c m\u1ea5y s\u1ed1 t\u1ef1 nhi\u00ean ch\u1eb5n bao g\u1ed3m 05 ch\u1eef s\u1ed1 t\u1eebng \u0111\u00f4i m\u1ed9t kh\u00e1c nhau.<\/p>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3i: <\/span><\/p>\n<p>a. Ta g\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean 04 ch\u1eef s\u1ed1 l\u00e0 n = a1a2a3a4. \u0110\u1ec3 c\u00f3 \u0111\u01b0\u1ee3c s\u1ed1 n nh\u01b0 v\u1eady th\u00ec ch\u00fang ta ph\u1ea3i ch\u1ecdn song song c\u00e1c s\u1ed1 a1, a2, a3, a4. Trong \u0111\u00f3 ta c\u00f3:<\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a1 c\u00f3 t\u1ed5ng c\u1ed9ng 6 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a2 c\u00f3 t\u1ed5ng c\u1ed9ng 5 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a3 c\u00f3 t\u1ed5ng c\u1ed9ng 4 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a4 c\u00f3 t\u1ed5ng c\u1ed9ng 3 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u00ec ch\u00fang ta c\u00f3 t\u1ed5ng c\u1ed9ng l\u00e0: 6 x 5 x 4 x 3 = 360 s\u1ed1 n mu\u1ed1n t\u00ecm.<\/span><\/p>\n<figure id=\"attachment_299182\" aria-describedby=\"caption-attachment-299182\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-299182 size-full\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-23.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-23\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-23.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-23-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-23-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-299182\" class=\"wp-caption-text\">V\u00ed d\u1ee5 minh h\u1ecda c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p<\/figcaption><\/figure>\n<p>b. Ta g\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean ch\u1eb5n bao g\u1ed3m 05 s\u1ed1 l\u00e0 n = a1a2a3a4a5. Trong \u0111\u00f3 ta c\u00f3:<\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a5 c\u00f3 \u0111\u00fang 1 c\u00e1ch ch\u1ecdn l\u00e0 2.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a1 c\u00f3 t\u1ed5ng c\u1ed9ng 5 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a2 c\u00f3 t\u1ed5ng c\u1ed9ng 4 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a3 c\u00f3 t\u1ed5ng c\u1ed9ng 3 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a4 c\u00f3 t\u1ed5ng c\u1ed9ng 2 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u00ec s\u1ed1 n mu\u1ed1n t\u00ecm l\u00e0 1 x 2 x 3 x 4 x 5 = 120 s\u1ed1.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 3<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Cho m\u1ed9t t\u1eadp h\u1ee3p A g\u1ed3m c\u00e1c s\u1ed1 l\u00e0 0, 1, 2, 3, 4, 5, 6. T\u1eeb t\u1eadp h\u1ee3p A n\u00e0y c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp \u0111\u01b0\u1ee3c m\u1ea5y s\u1ed1 t\u1ef1 nhi\u00ean g\u1ed3m 05 ch\u1eef s\u1ed1 t\u1eebng \u0111\u00f4i m\u1ed9t kh\u00e1c nhau v\u00e0 \u0111\u1ea3m b\u1ea3o s\u1ed1 5 v\u00e0 s\u1ed1 2 kh\u00f4ng \u0111\u1ee9ng b\u00ean c\u1ea1nh nhau.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3i:<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> T\u00ecm ra s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 05 ch\u1eef s\u1ed1 kh\u00e1c nhau t\u1eebng \u0111\u00f4i m\u1ed9t t\u00f9y \u00fd:<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">S\u1ed1 t\u1ef1 nhi\u00ean g\u1ed3m 05 ch\u1eef s\u1ed1 kh\u00e1c nhau v\u1edbi \u0111\u00f4i m\u1ed9t t\u00f9y \u00fd c\u00f3 d\u1ea1ng l\u00e0 n = a1a2a3a4a5. Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a1 c\u00f3 t\u1ed5ng c\u1ed9ng l\u00e0 6 c\u00e1ch \u0111\u1ec3 ch\u1ecdn (a1 \u2260 0).<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a2 c\u00f3 t\u1ed5ng c\u1ed9ng 6 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a3 c\u00f3 t\u1ed5ng c\u1ed9ng 5 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a4 c\u00f3 t\u1ed5ng c\u1ed9ng 4 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a5 c\u00f3 t\u1ed5ng c\u1ed9ng 3 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u00ec ch\u00fang ta c\u00f3 6 x 6 x 5 x 4 x 3 = 2169 s\u1ed1 t\u1ef1 nhi\u00ean.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299183 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-24.jpg\" alt=\"cong-thuc-to-hop-chinh-hop-24\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-24.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-24-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-to-hop-chinh-hop-24-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<ol start=\"2\">\n<li><span style=\"font-weight: 400;\"> T\u00ecm ra s\u1ed1 t\u1ef1 nhi\u00ean g\u1ed3m 05 ch\u1eef s\u1ed1 kh\u00e1c nhau t\u1eebng \u0111\u00f4i m\u1ed9t v\u00e0 c\u00f3 s\u1ed1 2 v\u1edbi 5 kh\u00f4ng \u0111\u01b0\u1ee3c \u0111\u1ee9ng c\u1ea1nh nhau:<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3 s\u1eed ta c\u00f3 s\u1ed1 2 v\u1edbi s\u1ed1 5 l\u00e0 m\u1ed9t ch\u1eef s\u1ed1 a ng\u1eabu nhi\u00ean. Ch\u00fang ta s\u1ebd t\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 04 ch\u1eef s\u1ed1:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Tr\u01b0\u1eddng h\u1ee3p 1: a1 = a<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a1 c\u00f3 t\u1ed5ng c\u1ed9ng 5 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a2 c\u00f3 t\u1ed5ng c\u1ed9ng 4 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a4 c\u00f3 t\u1ed5ng c\u1ed9ng 3 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u00ec ch\u00fang ta s\u1ebd c\u00f3 5 x 4 x 3 = 60 s\u1ed1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Tr\u01b0\u1eddng h\u1ee3p 2: a1 \u2260 a n\u00ean:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a1 c\u00f3 t\u1ed5ng c\u1ed9ng 4 c\u00e1ch \u0111\u1ec3 ch\u1ecdn (V\u00ec a1\u00a0 \u2260 0,2,5).<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">gi\u1ea3 s\u1eed a2 = a th\u00ec c\u00f3 3 v\u1ecb tr\u00ed cho s\u1ed1 a.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a3 c\u00f3 t\u1ed5ng c\u1ed9ng 4 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a4 c\u00f3 t\u1ed5ng c\u1ed9ng 3 c\u00e1ch \u0111\u1ec3 ch\u1ecdn.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady ta s\u1ebd c\u00f3 4 x 3 x 4 x 3 = 204. M\u00e0 s\u1ed1 2 v\u00e0 s\u1ed1 5 c\u00f3 th\u1ec3 ho\u00e1n \u0111\u1ed5i v\u1ecb tr\u00ed cho nhau. V\u00ec th\u1ebf n\u00ean suy ra ta c\u00f3: 204 x 2 = 408 s\u1ed1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Theo y\u00eau c\u1ea7u b\u00e0i to\u00e1n th\u00ec: 2160 &#8211; 408 = 1572 c\u00e1ch.<\/span><\/p>\n<p>Qua nh\u1eefng b\u00e0i t\u1eadp tr\u00ean, c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 hi\u1ec3u c\u00e1ch \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c trong to\u00e1n h\u1ecdc. \u0110\u00f3 l\u00e0 c\u00f4ng th\u1ee9c t\u00ednh ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, ho\u00e1n v\u1ecb trong c\u00e1c b\u00e0i to\u00e1n c\u1ee5 th\u1ec3. T\u1eeb \u0111\u00f3 c\u00e1c b\u1ea1n s\u1ebd l\u00e0m b\u00e0i t\u1eadp nhanh ch\u00f3ng v\u00e0 ti\u1ebfp thu ki\u1ebfn th\u1ee9c nhanh h\u01a1n.<\/p>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb l\u00e0 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n \u1edf THPT. C\u00f4ng th\u1ee9c n\u00e0y xu\u1ea5t hi\u1ec7n trong m\u1ed9t v\u00e0i \u0111\u1ec1 thi t\u1ed1t nghi\u1ec7p THPT trong nhi\u1ec1u n\u0103m qua. V\u00ec v\u1eady, c\u00e1c b\u1ea1n h\u1ecdc sinh ph\u1ea3i n\u1eafm ch\u1eafc c\u00f4ng th\u1ee9c t\u00ednh t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p tr\u00ean \u0111\u1ec3 thu\u1eadn ti\u1ec7n cho qu\u00e1 tr\u00ecnh m\u00ecnh \u00f4n thi v\u00e0 l\u00e0m c\u00e1c b\u00e0i thi quan tr\u1ecdng.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Tham kh\u1ea3o b\u00e0i vi\u1ebft li\u00ean quan:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-chu-nhat\/\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt ch\u00ednh x\u00e1c nh\u1ea5t<\/a><\/strong><\/li>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/vn-doc\/\">VnDoc \u2013 Gi\u1ea3i b\u00e0i t\u1eadp META Studio<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ed9 c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p, ho\u00e1n v\u1ecb lu\u00f4n khi\u1ebfn c\u00e1c b\u1ea1n h\u1ecdc sinh THPT d\u1ec5 nh\u1ea7m l\u1eabn gi\u1eefa c\u00e1c \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n ch\u00ednh x\u00e1c. Trong qu\u00e1 tr\u00ecnh h\u1ecdc th\u00ec c\u00e1c b\u1ea1n ph\u1ea3i ph\u00e2n bi\u1ec7t r\u00f5 ba lo\u1ea1i c\u00f4ng th\u1ee9c n\u00e0y th\u00ec m\u1edbi l\u00e0m b\u00e0i t\u1eadp v\u00e0 b\u00e0i thi hi\u1ec7u [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":299184,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-297318","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>B\u1ed9 c\u00f4ng th\u1ee9c Ho\u00e1n v\u1ecb - Ch\u1ec9nh h\u1ee3p - T\u1ed5 h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t<\/title>\n<meta name=\"description\" content=\"C\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea7n n\u1eafm c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p \u0111\u1ec3 l\u00e0m b\u00e0i t\u1eadp v\u00e0 \u00f4n thi THPT hi\u1ec7u qu\u1ea3. 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