Question 1081231: I have a league with 14 teams. Our league plays once a week. How many weeks are needed for each team to play each other once?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let's say there are two empty slots for you to fill. The first slot has 14 choices to pick from while the second slot has 13 choices. This is because you can't pick the same team twice.
Multiplying these values gives 14*13 = 182 different ways to pick two teams if order mattered.
However, order does NOT matter. The only thing that matters is the overall group chosen. For instance, let's say the league is composed of the team A through team N to represent the 14 teams. Choosing team A first and then team C is the same as choosing C first, then team A next. In set notation form, we can say {A,C} = {C,A}. Despite the order, the group is the same. If you factor in home field advantage, then order would matter; however, the instructions state "each team to play each other once" so the location is irrelevant.
Based on that example above, you can see that we're double counting. To correct for this, divide by 2 to get 182/2 = 91
So you'll need 91 weeks to play out the 91 different combinations.
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