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

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?

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.

Answer 3

To determine the number of different committees of 6 people that can be selected from this group, where there must be an equal number of men and women on each committee, you need to consider the combinations of men and women that can be chosen. Here's how you can break it down:

Step 1: Calculate the number of ways to select 3 men from the group of 8 men.
You can use the combination formula, which is denoted by "nCr" and gives the number of ways to choose "r" objects from a set of "n" objects without considering the order.

In this case, you want to choose 3 men from a group of 8 men, so you can calculate it as:
8C3 = (8!)/(3!(8-3)!) = 56

This means there are 56 different ways to choose 3 men from this group.

Step 2: Calculate the number of ways to select 3 women from the group of 10 women.
Using the same combination formula, you can calculate it as:
10C3 = (10!)/(3!(10-3)!) = 120

This means there are 120 different ways to choose 3 women from this group.

Step 3: Multiply the number of ways to choose men and women together.
Since you want committees where there is an equal number of men and women, you need to multiply the number of ways to choose men (56) by the number of ways to choose women (120):
56 * 120 = 6720

So, there are 6720 different committees of 6 people that can be selected from this group, where there is an equal number of men and women on each committee.

I hope this explanation helps! Feel free to ask any additional questions.