PUMaC 2024 · 组合（B 组） · 第 7 题
PUMaC 2024 — Combinatorics (Division B) — Problem 7
题目详情
- It is election year in PUMACland, and for the presidential election there are 27 people voting for either Vraj Patel or Vedant Shah. Each voter selects a candidate uniformly at random, and their ballots are labeled 1 through 27. The election takes place as a series of rounds. In each round, the surviving ballots are sorted by label and separated into consecutive groups of three. From each group, the person with 1 the most votes wins, and exactly one of the ballots bearing the winner’s name is allowed to proceed to the next round. This procedure continues until a single ballot remains, and the person whose name is on the ballot wins. Alice, Bob, and Carol submitted ballots numbered 1, 15, and 27, respectively. Suppose that Alice, Bob, and Carol had all flipped their votes. If the probability that the outcome of the a election would have changed is for relatively prime positive integers a, b , find a + b . b
解析
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Original Explanation
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