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

This means it must have 3 men and 3 women

For the men: 10 options for the first spot, 9 options for second, 8 options for last spot, to get 10 x 9 x 8 or 720

For the women: Do the same thing to get 15 x 14 x 13 or 2730

2730 + 720 = 3450

This problem can be written as 15P3 + 10P3