求教， 排列组合题

qingdaonycS

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

参考答案为D ， 我算了好几遍是 E， 哪位大侠讲解一下？ 多谢！

qingdaonycS

非常感谢！我是如此思路 看来错了三男C(3,5) + 三女C(3,5) + 两男一女C(2,5)*

C(1,5) +两女一男C(2,5)* C(1,5) = 120

mereiful

C(10,3)-C(5,1)*C(8,1)=120-40=80

1，从10人里挑3个C(10,3)；

2，每组里挑2个C(5,1)，剩下1个从剩下8人里选。