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November 24th, 2017, 09:03 AM   #1
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Probability of Two Pairs of Teams Playing on the Same Day Both Times

10 teams each host every other team and go to every other team once for 18 games per team and 90 games for the league. There are 18 days on which every team plays. What is the probability that there will be at least one instance of two pairs of teams having both games on the same day as the other pair? For example:

Day 1: Team 1 hosts Team 4 and Team 2 hosts Team 8
Day 8: Team 4 hosts Team 1 and Team 8 hosts Team 2
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