how many committee of five people can be chosen from 20 men and 12 women if a) exactly three men must be on each committee

Question

b) at least four women on each committee

Answer 1

Ahh, I see you fixed the problem from your earlier post.

a) 20 men, 12 women, choose 5, with exactly 3 men
= C(20,3) x C(12,2)
= 2053(66)
= 135498

b) at least 4 women
---> 4 women or 5 women

= C(20,1) x C(12,4) + C(20,0) x C(12,5)
= 20(495) + 1(792)
= 10692

check my arithmetic

Answer 2

a) 20 men, 12 women, choose 5, with exactly 3 men
= C(20,3) x C(12,2)
= 2053(66)
= 135498

b) at least 4 women
---> 4 women or 5 women

= C(20,1) x C(12,4) + C(20,0) x C(12,5)
= 20(495) + 1(792)
= 10692