## Quick Question

Suppose that you are trying to schedule 3 games between 6 teams (A, B, C, D, E, and F) that will occur simultaneously. Which of the following are feasible schedules? Select all that apply.

Explanation Each of the teams has to play exactly one of the other teams for the games to occur simultaneously. In the second option, C is playing twice, which is impossible. In the fourth option, B and C are both playing twice.

How many different feasible schedules are there?

Explanation There are 15 different feasible schedules. We can count them by observing that A can play any of the 5 teams. Once this is fixed, we have 4 teams left. There are 3 ways to make two pairs out of 4 teams. So in total, there are 5\*3 = 15 different schedules. Here is a list of all of them: A plays B, C plays D, E plays F A plays B, C plays E, D plays F A plays B, C plays F, D plays E A plays C, B plays D, E plays F A plays C, B plays E, D plays F A plays C, B plays F, D plays E A plays D, B plays C, E plays F A plays D, B plays E, C plays F A plays D, B plays F, C plays E A plays E, B plays C, D plays F A plays E, B plays D, C plays F A plays E, B plays F, C plays D A plays F, B plays C, D plays E A plays F, B plays D, C plays E A plays F, B plays E, C plays D