PUMaC 2019 · 组合（B 组） · 第 1 题
PUMaC 2019 — Combinatorics (Division B) — Problem 1
题目详情
- How many ways can you arrange 3 Alice’s, 1 Bob, 3 Chad’s, and 1 David in a line if the Alice’s are all indistinguishable, the Chad’s are all indistinguishable, and Bob and David want to be adjacent to each other? (In other words, how many ways can you arrange 3 A’s, 1 B, 3 C’s, and 1 D in a row where the B and D are adjacent?)
解析
- How many ways can you arrange 3 Alice’s, 1 Bob, 3 Chad’s, and 1 David in a line if the Alice’s are all indistinguishable, the Chad’s are all indistinguishable, and Bob and David want to be adjacent to each other? (In other words, how many ways can you arrange 3 A’s, 1 B, 3 C’s, and 1 D in a row where the B and D are adjacent?) Proposed by Nathan Bergman. Answer: 280 . Solution: It’s 7! ∗ 2 = 280 . 3!3!