Expert: Scott A Wilson - 7/6/2011

Question
I've tried to solve this problem but i can't. Please help me.

*How many mixed doubles tennis teams can be formed from 10 players, where 6 are male and 4 are female?

Answer
For each game, we need two men and two women.

For choosing 2 men it would be 6 choose 2 = (6*5)/(2*1) = 30/2 = 15.
For choosing 2 women it would be 4 choose 2 = (4*3)/(2*1) = 12/2 = 6.

Once two men and two women are selected, say M1, M2, W1, and W2,
there could be M1-W1 vs. M2-W2 or M1-W2 vs. M2-W1, so that doubles the number.

Thus, the answer is 15*6*2 = 180.

If we worried about which team got which side of the tennis court,
there would be twice that many.

That is since once we have M1, M2, W1, and W2, the choices would be
M1-W1 vs. M2-W2, M1-W2 vs. M2-W1, M2-W1 vs. M1-W2, and M2-W2 vs. M1-W1.
That is 4 ways for each pair, so the total is 15*6*4 = 360.