Question

Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have the same number of men and women?

Answer 1

Answer: 120

Explanation:

To form a committee with 6 members that contains the same number of men and women, we must choose 3 men and 3 women from the 10 men and 15 women that are available. This can be done in a total of ${10\choose3} = 120$ ways. Therefore, there are a total of 120 ways to form a committee with 6 members that contains the same number of men and women. I hope this helps! Do you have any other questions?