Cov qauv sib xyaw ua ke yog: nCr = n! / ((n u2013 r)! r!) n = tus naj npawb ntawm cov khoom.
Ntawm no, koj ua piv txwv ua ke ua ke li cas? Cov mis sib xyaw ua ke yog siv los nrhiav tus naj npawb ntawm txoj hauv kev xaiv cov khoom los ntawm kev sau, xws li qhov kev txiav txim ntawm kev xaiv tsis muaj teeb meem.
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Formula rau kev sib xyaw.
Combination Formula | nCr=n!(nu2212r)!r! nCr = n! (n u2212 r) ! r kev! |
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Combination Formula siv Permutation | C(n, r) = P(n, r)/ r! |
Dab tsi ua ke nrog piv txwv? Kev sib xyaw ua ke yog ib qho kev xaiv ntawm tag nrho lossis ib feem ntawm cov khoom siv, tsis hais txog qhov kev txiav txim ntawm cov khoom raug xaiv. Piv txwv li, xav tias peb muaj peb tsab ntawv: A, B, thiab C. … Txhua qhov kev xaiv yuav yog ib qho piv txwv ntawm kev sib xyaw. Tag nrho cov npe ntawm cov kev xaiv tau yuav yog: AB, AC, thiab BC.
Tsis tas li ntawd, qhov yooj yim tshaj plaws los xam cov kev sib txuas yog dab tsi?
Tus nqi ntawm 8C5 yog dab tsi? (n-r)! 8c5 =8!
Tus nqi ntawm 5c 2 yog dab tsi?
5 XYOO 2 = 10 qhov ua tau ua ke. 10 yog tus naj npawb tag nrho ntawm txhua qhov kev sib txuas ua ke rau kev xaiv 2 lub ntsiab lus ntawm ib lub sijhawm los ntawm 5 cov ntsiab lus sib txawv yam tsis xav txog qhov kev txiav txim ntawm cov ntsiab lus hauv kev txheeb cais & kev soj ntsuam qhov tshwm sim lossis kev sim.
Tus nqi ntawm 8 ua ke 5 yog dab tsi? (n-r)! = (8 – 5) (8-5) ! = 3!
Tus nqi ntawm 10 C 3 yog dab tsi? C3 = 10 ib! / 3! (7) koj!
Tus nqi ntawm 6C4 yog dab tsi?
(n-r)! r kev! 6c4 = 6!
Thiab tus nqi ntawm 7v4 yog dab tsi? Summary : Lub permutation los yog ua ke ntawm 7C4 is 35.
Cov lus teb ntawm 5C3 yog dab tsi?
Combinatorics thiab Pascal's Daim duab peb sab
0c0 = 1 | ||
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2c0 = 1 | 2c1 = 2 | |
3c0 = 1 | 3c2 = 3 | |
4c0 = 1 | 4c1 = 4 | 4c2 = 6 |
5c1 = 5 | 5C3 = np 10 |
3C2 txhais li cas? 3v2 ua. =3! (2!) (3–2)! =3!
Tus nqi ntawm 10 C 4 yog dab tsi?
Cov lus piav qhia ib qib zuj zus:
10 xaiv 4 = 201 qhov ua tau ua ke. 201 yog tus naj npawb tag nrho ntawm txhua qhov kev sib txuas ua ke rau kev xaiv 4 lub ntsiab lus ntawm ib lub sijhawm los ntawm cov ntsiab lus sib txawv yam tsis xav txog qhov kev txiav txim ntawm cov ntsiab lus hauv kev txheeb cais & kev tshawb fawb txog qhov tshwm sim lossis kev sim.
Tus nqi ntawm 6 C 2 yog dab tsi?
Sib 6C2. 6C2 = 6!/(6-2) ! 2 ib! = 6 ib! /4!
Muaj pes tsawg qhov sib xyaw ntawm cov lej 1 2 3 4 muaj? Kev piav qhia: Yog tias peb tab tom saib cov lej peb tuaj yeem tsim siv tus lej 1, 2, 3, thiab 4, peb tuaj yeem suav tias txoj hauv qab no: rau txhua tus lej (txhiab, pua, kaum, ib tus), peb muaj 4. kev xaiv ntawm tus lej. Thiab yog li peb tuaj yeem tsim 4 × 4 × 4 × 4 = 44 =256 tus xov tooj.
Koj yuav daws 10 Factorials li cas? ua 362,880. Sim xam 10! 10 ib! = 10 x9!
4C1 yog dab tsi?
4 XAIV 1 = 4 ua tau ua ke. Kev piav qhia: Tam sim no nws tshwm sim li cas Yog li, 4 yog tag nrho ntawm txhua qhov kev sib txuas ua ke rau kev xaiv 1 lub ntsiab lus ntawm ib lub sijhawm los ntawm 4 cov ntsiab lus sib txawv yam tsis xav txog qhov kev txiav txim ntawm cov ntsiab lus hauv kev txheeb cais & kev soj ntsuam qhov tshwm sim lossis kev sim. Ua tsaug 0.
Tus nqi ntawm 5C1 yog dab tsi? Combinatorics thiab Pascal's Daim duab peb sab
2c0 = 1 | 2c2 = 1 | |
3c0 = 1 | 3c2 = 3 | |
4c0 = 1 | 4c1 = 4 | 4c3 = 4 |
5C1 = np 5 | 5c3 = 10 |
Tus nqi ntawm 6P4 yog dab tsi?
⇒6P4 =6! (6-4) ! =6!
15c3 ua ke yog dab tsi? 0
4C2 ua ke yog dab tsi?
Peb paub tias cov qauv siv los daws cov kab lus sib xyaw ua ke yog muab los ntawm: … Hloov n = 4 thiab r = 2 hauv cov qauv saum toj no, 4C2 = 4!/ 2! (4–2) Xee! 4 = 2!
7c3 yog dab tsi? 8 x 7 x 6 = 336. C7,3 =7!(3!)(7−3)= 7!
Koj daws 5P2 li cas?
5 np2 = 5! / (5–2). 5x4x 3! / 3!
Koj ua li cas 5C3 ntawm lub laij lej?
10C7 yog dab tsi?
⇒10C7 =10! 7! ×3! =10×9×8×7×6×5×4×3×2 7×6×5×4×3×2 ×3×2. =10×9×83×2=120.
5C4 ua ke yog dab tsi?
nCr=(r!)(n−r)! tsis yog! yog, 5c4(4!)(