PUMaC 2024 · 团队赛 · 第 15 题

PUMaC 2024 — Team Round — Problem 15

There are 10 teams, named T through T , participating in a draft in which there are 20 1 10 players available, named P through P . Suppose each team independent of the others has 1 20 uniform random preference on the 20 players. Team T will draft their favorite player, and 1 then each subsequent team T , . . . , T draft their favorite player among the ones not already 2 10 drafted. Each team drafts exactly one player. Given that P is among the 10 favorite players 1 m for each team, the probability that P is drafted can be written as where m and n are 1 n coprime positive integers. Find m + n . Team: Write answers in table below: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 M 2

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