HMMT 二月 2003 · GEN1 赛 · 第 1 题

英文解析

1. 10 people are playing musical chairs with n chairs in a circle. They can be seatedin 7! ways (assuming only one person fits on each chair, of course), where differentarrangements of the same people on chairs, even rotations, are considered different.
   Find n .
   Solution: 4
   The number of ways 10 people can be seated on n chairs is n ! multiplied by the numberof ways one can choose n people out of 10. Hence we must solve 7! = n ! · 10! / ( n ! · (10 −
   n )!). This is equivalent to (10 − n )! = 10! / 7! = 8 · 9 · 10 = 720 = 6!. We therefore haven = 4.