MathDB

5

Part of 2019 CHMMC (Fall)

Problems(1)

2019 Fall Team #5

Source:

4/17/2022
A tournament has 55 players and is in round-robin format (each player plays each other exactly once). Each game has a 13\frac13 chance of player AA winning, a 13\frac13 chance of player BB winning, and a13 \frac13 chance of ending in a draw. The probability that at least one player draws all of their games can be written in simplest form as m3n\frac{m}{3^n} where m,nm, n are positive integers. Find m+nm + n.
combinatorics