how many matches are played

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so the question is the are a total of 16 teams. Each team will play each other once so each team will play 15 matches since they can't play themselves. How many matches in total are played?

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1 Answer

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There are 16 teams that can be chosen as the first team in a game, and for each team, 15 teams they can play. But this approach overcounts by a factor of 2, because you have counted team A (first player) playing team B (second player) as well as team B (first player) playing team A (second player). Thus the answer is $16 \times 15/2 = 120$.

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