Prep-T1-43(PS)

[邁向高等學府]

A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

(A)16
(B)24
(C)26
(D)30
(E)32

Ans:E

How the "32" is caculated??
謝謝大大

[hey]

先將couple都選入committe的組合方法找出來, 如果couple都必需選入的話, 請先將其當做一個單位, 因為3個中已選了2個, 現在只有在其他的6位中再選1位, 而每一對couple都與其他6位的組合為6種,而有4對, 因此即為6*4=24種
而全部的組合排列為8!/3!5!=56
committe中不能有couple的組合=全部的組合-committe中有couple的組合
56-24=32
所以答案為(E)