急!!!!!PERMUTATION &COMBINATION

[匿名]

2011-01-06 5:50 am

in a parent teacher association,there are 5 couples.a project team of 4 people is going to be selected from the couples.find the no. of ways to from the team if
a)the team consists of no couples
b)the team consists of exactly 1 couple
THX!!!!!!!!!!!!!!!!!!!!!!

更新1:

不過我都係唔明2^4果一個可唔可以中文解一次??? THX!

回答 (1)

用戶2053

2011-01-06 6:36 am

✔ 最佳答案

a)Choose 4 couples from 5 couples : 5C4 ways , then choose 1 people from each couples , 2^4 ways ,(5C4)(2^4) = 80 ways.b)Choose 1 couples from 5 couples : 5C1 ways , then choose 3 couples from the remain 4 couples : 4C3 ways , then choose 1 people from each : 2^3 ways.(5C1)(4C3)(2^3) = 160 ways.

2011-01-05 22:47:56 補充：
Corrections :

b)

Choose 1 couples from 5 couples : 5C1 ways , then choose 2 couples from the remain 4 couples : 4C2 ways , then choose 1 people from each : 2^2 ways.
(5C1)(4C2)(2^2) = 120 ways.

Sorry!

2011-01-05 23:02:33 補充：
a)

5 對 couples 選 4 人 , 4 人中無任何 2 人是couples。
所以 4 人來自不同 couples , 5 對 couples 選 4 對有 5C4 ways ,
然後從這4 對 couples 中每對各選 1 人 ,因為每對couple 有 2 人選擇 ,
4 對就有 2 x 2 x 2 x 2 = 2^4 個選擇。

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