{"id":23763,"date":"2023-12-06T08:52:48","date_gmt":"2023-12-06T08:52:48","guid":{"rendered":"https:\/\/masterskills.org\/blog\/phep-hoan-vi-permutation-la-gi-dac-diem.html"},"modified":"2023-12-22T09:04:27","modified_gmt":"2023-12-22T02:04:27","slug":"phep-hoan-vi-permutation-la-gi-dac-diem","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/phep-hoan-vi-permutation-la-gi-dac-diem.html","title":{"rendered":"Ph\u00e9p ho\u00e1n v\u1ecb (Permutation) l\u00e0 g\u00ec? \u0110\u1eb7c \u0111i\u1ec3m"},"content":{"rendered":"
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\u1ea2nh minh h\u1ecda. Ngu\u1ed3n: e-GMAT.<\/p>\n<\/div>\n<\/div>\n

Ph\u00e9p ho\u00e1n v\u1ecb<\/font><\/b><\/h2>\n

Kh\u00e1i ni\u1ec7m<\/b><\/p>\n

Ph\u00e9p ho\u00e1n v\u1ecb <\/b>ti\u1ebfng Anh l\u00e0 Permutation.<\/b><\/p>\n

Ph\u00e9p ho\u00e1n v\u1ecb <\/b>l\u00e0 m\u1ed9t ph\u00e9p t\u00ednh to\u00e1n v\u1ec1 s\u1ed1 l\u01b0\u1ee3ng c\u00e1ch m\u00e0 m\u1ed9t ph\u00e9p t\u00ednh c\u1ee5 th\u1ec3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp, nh\u1edd s\u1ef1 thay \u0111\u1ed5i trong th\u1ee9 t\u1ef1 s\u1eafp x\u1ebfp.<\/p>\n

\u0110\u1eb7c \u0111i\u1ec3m c\u1ee7a Ph\u00e9p ho\u00e1n v\u1ecb<\/font><\/b><\/h3>\n

C\u00f4ng th\u1ee9c c\u1ee7a ph\u00e9p ho\u00e1n v\u1ecb nh\u01b0 sau:<\/p>\n

P(n, r) = n!\/(n-r)!<\/b><\/p>\n

Trong \u0111\u00f3:<\/i><\/p>\n

n = t\u1ed5ng s\u1ed1 m\u1ee5c trong t\u1eadp h\u1ee3p; r = ph\u1ea7n t\u1eed ho\u00e1n v\u1ecb; “!” l\u00e0 ph\u00e9p t\u00ednh giai th\u1eeba<\/p>\n

C\u00f4ng th\u1ee9c tr\u00ean c\u00f3 ngh\u0129a l\u00e0: “B\u1ea1n c\u00f3 th\u1ec3 s\u1eafp x\u1ebfp ‘r’ theo bao nhi\u00eau c\u00e1ch t\u1eeb m\u1ed9t t\u1eadp h\u1ee3p ‘n’ v\u1edbi th\u1ee9 t\u1ef1 kh\u00e1c bi\u1ec7t?” M\u1ed9t ph\u00e9p ho\u00e1n v\u1ecb c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng tay, trong \u0111\u00f3 t\u1ea5t c\u1ea3 c\u00e1c ph\u00e9p ho\u00e1n v\u1ecb c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c vi\u1ebft ra. T\u1ed5 h\u1ee3p (combination) \u0111\u00f4i khi b\u1ecb nh\u1ea7m l\u1eabn v\u1edbi ho\u00e1n v\u1ecb. Trong ho\u00e1n v\u1ecb, th\u1ee9 t\u1ef1 \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng, c\u00f2n trong t\u1ed5 h\u1ee3p, th\u1ee9 t\u1ef1 kh\u00f4ng \u0111\u00f3ng vai tr\u00f2 n\u00e0o.<\/p>\n

V\u00ed d\u1ee5 v\u1ec1 ho\u00e1n v\u1ecb<\/font><\/b><\/h3>\n

M\u1ed9t v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n \u0111\u1ec3 h\u00ecnh dung m\u1ed9t ho\u00e1n v\u1ecb l\u00e0 s\u1ed1 c\u00e1ch s\u1eafp x\u1ebfp m\u1ed9t chu\u1ed7i c\u1ee7a m\u1ed9t b\u00e0n ph\u00edm 3 ch\u1eef s\u1ed1. S\u1eed d\u1ee5ng c\u00e1c ch\u1eef s\u1ed1 t\u1eeb 0 \u0111\u1ebfn 9 v\u00e0 ch\u1ec9 s\u1eed d\u1ee5ng m\u1ed9t ch\u1eef s\u1ed1 c\u1ee5 th\u1ec3 tr\u00ean b\u00e0n ph\u00edm, s\u1ed1 l\u1ea7n ho\u00e1n v\u1ecb l\u00e0 P(10,3) = 10!\/(10-3)! = 10!\/7! = 10 x 9 x 8 = 720. Trong v\u00ed d\u1ee5 n\u00e0y, th\u1ee9 t\u1ef1 \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng. V\u1edbi ho\u00e1n v\u1ecb, (1,3,2) kh\u00e1c (1,2,3), c\u00f2n \u0111\u1ed1i v\u1edbi t\u1ed5 h\u1ee3p, (1,3,2) v\u00e0 (1,2,3) gi\u1ed1ng nhau.<\/p>\n

M\u1ed9t v\u00ed d\u1ee5 kh\u00e1c nh\u01b0 sau: Ki\u1ec3m tra t\u1ea5t c\u1ea3 c\u00e1c c\u00e1ch kh\u00e1c nhau trong \u0111\u00f3 m\u1ed9t c\u1eb7p \u0111\u1ed1i t\u01b0\u1ee3ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ch\u1ecdn t\u1eeb 5 \u0111\u1ed1i t\u01b0\u1ee3ng c\u00f3 th\u1ec3 ph\u00e2n bi\u1ec7t \u0111\u01b0\u1ee3c nh\u01b0 c\u00e1c ch\u1eef c\u00e1i A, B, C, D v\u00e0 E. N\u1ebfu xem x\u00e9t c\u1ea3 v\u1ec1 th\u1ee9 t\u1ef1, th\u00ec ta s\u1ebd c\u00f3 20 k\u1ebft qu\u1ea3, g\u1ecdi l\u00e0 c\u00e1c ho\u00e1n v\u1ecb nh\u01b0 sau: AB, BA, AC, CA, AD, DA, AE, EA, BC, CB, BD, DB, BE, EB, CD, DC, CE, EC, DE, ED. Trong khi \u0111\u00f3, n\u1ebfu d\u00f9ng ph\u00e9p t\u1ed5 h\u1ee3p, ch\u1ec9 c\u00f3 10 t\u1eadp h\u1ee3p con kh\u00e1c nhau: AB, AC, AD, AE, BC, BD, BE, CD, CE v\u00e0 DE.<\/p>\n

Trong t\u00e0i ch\u00ednh v\u00e0 kinh doanh, l\u1ea5y hai v\u00ed d\u1ee5 nh\u01b0 sau. \u0110\u1ea7u ti\u00ean, gi\u1ea3 s\u1eed m\u1ed9t nh\u00e0 qu\u1ea3n l\u00ed danh m\u1ee5c \u0111\u1ea7u t\u01b0 \u0111\u00e3 s\u00e0ng l\u1ecdc 100 c\u00f4ng ty cho m\u1ed9t qu\u0129 m\u1edbi s\u1ebd bao g\u1ed3m 25 c\u1ed5 phi\u1ebfu. 25 c\u1ed5 phi\u1ebfu n\u00e0y c\u00f3 v\u1ecb th\u1ebf n\u1eafm gi\u1eef kh\u00f4ng b\u1eb1ng nhau, ngh\u0129a l\u00e0 c\u1ea7n ph\u1ea3i s\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 n\u1eafm gi\u1eef. S\u1ed1 c\u00e1ch s\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 n\u1eafm gi\u1eef trong qu\u0129 s\u1ebd l\u00e0: P(100,25) = 100!\/(100-25)! = 100!\/75! = 3.76E + 48. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 ng\u01b0\u1eddi qu\u1ea3n l\u00ed danh m\u1ee5c \u0111\u1ea7u t\u01b0 s\u1ebd ph\u1ea3i nghi\u00ean c\u1ee9u r\u1ea5t nhi\u1ec1u c\u00e1ch \u0111\u1ec3 x\u00e2y d\u1ef1ng qu\u0129 c\u1ee7a m\u00ecnh.<\/p>\n

M\u1ed9t v\u00ed d\u1ee5 kh\u00e1c nh\u01b0 sau: m\u1ed9t c\u00f4ng ty mu\u1ed1n x\u00e2y d\u1ef1ng m\u1ea1ng l\u01b0\u1edbi kho c\u1ee7a m\u00ecnh tr\u00ean to\u00e0n qu\u1ed1c. C\u00f4ng ty s\u1ebd cam k\u1ebft 3 \u0111\u1ecba \u0111i\u1ec3m trong s\u1ed1 5 \u0111\u1ecba \u0111i\u1ec3m c\u00f3 th\u1ec3. S\u1ed1 l\u01b0\u1ee3ng ho\u00e1n v\u1ecb l\u00e0: P (5,3) = 5! \/ (5-3)! = 5! \/ 2! = 60.<\/p>\n

(Theo\u00a0Investopedia <\/i>v\u00e0 Encyclopedia Britannica<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n Ph\u00e9p ho\u00e1n v\u1ecb (ti\u1ebfng Anh: Permutation) l\u00e0 m\u1ed9t ph\u00e9p t\u00ednh to\u00e1n v\u1ec1 s\u1ed1 l\u01b0\u1ee3ng c\u00e1ch m\u00e0 m\u1ed9t ph\u00e9p t\u00ednh c\u1ee5 th\u1ec3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp, nh\u1edd s\u1ef1 thay \u0111\u1ed5i trong th\u1ee9 t\u1ef1 s\u1eafp x\u1ebfp.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[414],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/23763"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=23763"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/23763\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=23763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=23763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=23763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}