Question 40
20 players are playing in a Super Smash Bros. Melee tournament. They are ranked $1-20$, and player $n$ will always beat player $m$ if $n \lt m$. Out of all possible tournaments where each player plays 18 distinct other players exactly once, one is chosen uniformly at random. Find the expected number of pairs of players that win the same number of games.
Proposed by: Anders Olsen
Proposed by: Anders Olsen