求解一道数学题

teddyabc

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?


A.20
B.40
C.50
D.80
E.120
答案是D
而我得出的结果却是10*8*6=480
相差甚远啊，NN们能否一解释疑啊

teddyabc

原来是这个意思，灰常感谢！！

xiexiang

5对选3对，   10
然后三对里各选1个   2*2*2
10*8=80

你这种有大量重复
如1a2a3a   和2a3a1a  岂不是一样吗

卮言浅夏

480/3! = 80

The three people you selected as ABC would be the same composition as BCA, CAB, etc.

avalon9527

这类题目不能像你那么解答，你那么解答是有很多重复的。
这类题应该先选哪一对，再选这一对的哪一个人，实际上应该是C(3,5)*C(2,1)*C(2,1)*C(2,1)=80 这样才不会有重复。