How many committees?

Question

A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many can be formed if no person can serve on more than one committee?

Answer 1

C(9,4) * C(5,3) * C(2,2)

= 9! / 4!(9-4)! * 5! / 3!(5-3)! * 2! / 2!(2-2)!

= 9! / 4!5! * 5! / 3!2! * 2! / 2!0!

= (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1

=1260

1260 committees can be formed.