PUMaC 2017 · 组合（B 组） · 第 1 题
PUMaC 2017 — Combinatorics (Division B) — Problem 1
题目详情
- In how many different orders can the characters P U M α C be arranged such that the M is to the left of the α and the α is to the left of the C ?
解析
- With no restrictions there are 5! = 120 ways. Consider now just the M αC . There are 3! = 6 permutations of these alone, but only 1 of them is valid with the restrictions given. This is a subsequence of the overall string, and is as likely to appear as any other permutation. This we find that 5! / 3! = 20 is our final answer. Problem written by Zack Stier