PUMaC 2021 · 组合（B 组） · 第 1 题
PUMaC 2021 — Combinatorics (Division B) — Problem 1
题目详情
- A nonempty word is called pronounceable if it alternates in vowels (A, E, I, O, U) and conso- nants (all other letters) and it has at least one vowel. How many pronounceable words can be formed using the letters P, U, M, A, C at most once each? Words of length shorter than 5 are allowed.
解析
- A nonempty word is called pronounceable if it alternates in vowels (A, E, I, O, U) and conso- nants (all other letters) and it has at least one vowel. How many pronounceable words can be formed using the letters P, U, M, A, C at most once each? Proposed by: Daniel Carter Answer: 68 The number of vowels and consonants to choose which can be arranged to form a pronounceable word are: • 1 vowel, 0 consonants: 2 · 1 · 1 choices (2 choices of vowels, 1 of consonants, and 1 for order). • 1 V, 1 C: 2 · 3 · 2 choices. • 1 V, 2 C: 2 · 3 · 2 choices. • 2 V, 1 C: 1 · 3 · 2 choices. • 2 V, 2 C: 1 · 3 · 8 choices. • 2 V, 3 C: 1 · 1 · 12 choices. The total is 68.