Question

2) A group of 11 professors consists of 7 women and 4 men. Find the number of ways to (4 points) a) select a committee of 4 members from the group. (6 points) b) select a committee of 5 members from the group with 3 women and 2 men.

Answer 1

1) Group of 4 members
case 1 = 0 women 4 men = (7c0)*(4c4) = 1
case 2 = 1 women 3 men = (7c1)*(4c3) = 7*4=28
case 3 = 2 women 2 men = (7c2)*(4c2) = 21 * 6 = 126
case 4 = 3 women 1 men = (7c3)*(4c1) = 35 * 4 = 140
case 5 = 4 women 0 men = (7c4)*(4c0) = 35 *1 = 35

total number of ways = 1+28+126+140+35 = 330

2)
group of 5 members
number of women =3 and number of men =2
= 7c3 + 4c2 = 35 * 6 = 210 ways

if you like the answer please provide a thumbs up.