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Omni-MATH / 20 players are playing in a Super Smash Bros. Melee tournament. They are ranked…

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problem

20 players are playing in a Super Smash Bros. Melee tournament. They are ranked 1−201-20, and player nn will always beat player mm if n<mn<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.
Plain-text mathematical notation (without MathML)
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<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.
Original LaTeX notation
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 $n<m$. 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.

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Source and history

task_id
19be5862-fcb0-56dd-ac87-44d8fed06ea5
task_key
test--19be5862-fcb0-56dd-ac87-44d8fed06ea5
task_revision_id
1
config / split
/ test

Official source

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