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Six tennis players have signed-up for a round-robin tennis tournament. The first set of 3 matches will be played at 8am on Saturday and one possible game set-up follows: Because there is no distinction in the 3 courts where games are played (i.e. what really matters is who plays each other). note that the following set-up is considered the same as the example above: In how many unique ways can the first set of 3 matches be assigned? Provide an answer that utilizes permutations and/or combinations.

Solution

Let\'s choose the first match first.

There are 6C2 = 15 ways to do that.

Now, we have to choose on just 4 players, as 2 have playes already.

There are 4C2 = 6 ways to do that.

The remaining two players have to play each other, then.

Thus, there are 15*6 = 90 different ways. [ANSWER]