MathDB

31

Part of 2017 Harvard-MIT Mathematics Tournament

Problems(1)

2017 Guts #31: Imbalance of league

Source:

2/21/2017
A baseball league has 66 teams. To decide the schedule for the league, for each pair of teams, a coin is flipped. If it lands head, they will play a game this season, in which one team wins and one team loses. If it lands tails, they don't play a game that season. Define the imbalance of this schedule to be the minimum number of teams that will end up undefeated, i.e. lose 00 games. Find the expected value of the imbalance in this league.
combinatorics