Suppose that a department contains 10 men and 15 women. How many way are there to form a committee of 6 members if it must have the same number of men and women?

I decided to just figure out how many combination of men and women fit in their 3 allowed slots

Men:
10!/7! = 10*9*8 = 720

Women:
10!/12! = 15*14*13 = 2730

Thus:
720 + 2730 = 3450