This question just came to me as I was watching a football game.

There is a football league with 20 teams. Each team has to play every other team at home and away, which means each team will play a total of 38 games. All teams will play a game every weekend, and hence the season lasts for 38 weeks. Now, I am interested in following the 6 teams that are favored to win the league. What is the probability that on any given weekend during the season, there is at least one match involving 2 of my 6 favored teams?

What is the generalized solution for the same problem in a league with N teams and n favorites?

  • 1
    $\begingroup$ Do you mean to ask what the probability is that on every weekend of the season, two of your favorites will meet? Or the probability for just one weekend? Because the latter is $1-\frac{10*9*8*7*6*5}{10*10*10*10*10*10}$ which follows from the same analysis as in the Birthday problem. The probability of it not happening is the same as that of 6 teams(people) all being assigned different matches(birthdays), out of 10 available. See en.wikipedia.org/wiki/Birthday_problem $\endgroup$ Aug 23, 2013 at 15:11
  • $\begingroup$ @FanOfFourier: You just answered my question $\endgroup$
    – Max
    Aug 23, 2013 at 15:40


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