PUMaC 2024 · 组合（A 组） · 第 3 题

PUMaC 2024 — Combinatorics (Division A) — Problem 3

Joseph chooses a permutation of the numbers 1 , 2 , 3 , 4 , 5 , 6 uniformly at random. Then, he goes through his permutation, and deletes the numbers which are not the maximum among each of the preceding numbers. For example, if he chooses the permutation 3 , 2 , 4 , 5 , 1 , 6, then he deletes 2 and 1, leaving him with 3 , 4 , 5 , 6. The expected number of numbers remaining can be expressed as m/n for relatively prime positive integers m and n . Find m + n .

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