There are 10 women and 8 men in a club. How many different committees of 6 people can be selected from the group if equal numbers of men and women are to be on the committee?

Question

I think it would be 2, because half of 6 is 3, so 3 are men and 3 are women.
2 committees of 3 each would work, but 3 committees of 3 each would not since there are only 8 men. I can't figure out to put it into an equation to get 2 as the answer. (This sounds like something Edith Bunker would say, if you know who she is.)

Thanks for all your help.

Answer 1

This is a combination question

You want to choose 3 women from the 10 and 3 men from the 8

number of committees = C(10,3)*C(8,3)
= 120*56 = 6720

Answer 2

I can't figure out where you got the 120 and 56.