[求助]TT5-3

huangxiaoyan

Q3:

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

Hi_Cynthia

好，我来解一下
不用复杂的公式，浅显的说，总共5对夫妇，要选出3人，这3人当然不分顺序，题目要求不能存在一对夫妇在这3人里，所以说暂且把5对看为5个人，那么就是C（3，5）=5*4*3/3！=10，这样从哪组选人就确定了，再看，每组2个人-夫妇，选出的3组每组有2种可能，选夫，或选妇，所有2*2*2=8，选组和在选好的组里选谁去中间是相乘的关系，10*8=80
完毕

huangxiaoyan

多谢，非常清楚