HMMT 二月 2007 · COMB 赛 · 第 1 题

英文解析

1. [ 3 ] A committee of 5 is to be chosen from a group of 9 people. How many ways can it be chosen, if
   Biff and Jacob must serve together or not at all, and Alice and Jane refuse to serve with each other?
   ( )
   Answer: 41 . If Biff and Jacob are on the committee, there are = 35 ways for the other members 7
   ( )3
   to be chosen. Amongst these 35 possibilities, we reject the = 5 choices where both Alice and Jane 5
   ( )1
   are also serving. If Biff and Jacob are not serving, then there are = 21 ways to choose the remaining 7
   ( )5
   5 members. Again, we reject the = 10 instances where Alice and Jane are chosen, so the total is 5
   (35 − 5) + (21 − 10) = 41.3