HMMT 二月 2007 · TEAM2 赛 · 第 3 题
HMMT February 2007 — TEAM2 Round — Problem 3
题目详情
- [ 20 ] Five people are crowding into a booth against a wall at a noisy restaurant. If at most three canfit on one side, how many seating arrangements accomodate them all?
英文原题
[ 25 ] Deduce from the above that
BC
AD · AI
BI · DI
CI = 1 .
解析
英文解析
- [ 20 ] Five people are crowding into a booth against a wall at a noisy restaurant. If at most three canfit on one side, how many seating arrangements accomodate them all?
Answer: 240 . Three people will sit on one side and two sit on the other, giving a factor of two.
Then there are 5! ways to permute the people.