PUMaC 2015 · 组合（B 组） · 第 1 题

PUMaC 2015 — Combinatorics (Division B) — Problem 1

[ 3 ] A word is an ordered, non-empty sequence of letters, such as word or wrod . How many distinct 3-letter words can be made from a subset of the letters c, o, m, b, o , where each letter in the list is used no more than the number of times it appears?

解析

[ 3 ] A word is an ordered, non-empty sequence of letters, such as word or wrod . How many distinct 3-letter words can be made from a subset of the letters c, o, m, b, o , where each letter in the list is used no more than the number of times it appears? ( ) 3 Solution: There are · 3 = 9 three-letter words with 2 o ’s (we choose the positions of the 2 o ’s and then choose the third letter) and 4 · 3 · 2 = 24 words without an o for a total of 33 words. Author: Bill Huang