Question 578564: In a round-robin tournament, each team must play every other team once. How many games must be scheduled if there are 10 teams? If there are 20 teams? If there are n teams? [Hint: Use the idea of difference equations. Try to figure out how the number of games increases when one new team is added to the tournament.]
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Each of the 10 teams plays 9 other teams, and 10*9 = 90. However, we are counting each pair twice (Team A, B and Team B, A should be counted as one game) so we divide by 2 to get 45. Alternatively, you can write the number of ways as 10C2.
This generalizes so for 20 teams, the number of games would be 20C2 = 190, and for n teams, nC2.
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