How many committees of five people can be chosen from 20 men and 12 women such…
2015
How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women ?
- A.
75240
- B.
52492
- C.
41800
- D.
9900
Attempted by 53 students.
Show answer & explanation
Correct answer: B
Key idea: count committees by cases based on the number of women (3, 4, or 5).
3 women and 2 men: C(12,3) * C(20,2) = 220 * 190 = 41800
4 women and 1 man: C(12,4) * C(20,1) = 495 * 20 = 9900
5 women and 0 men: C(12,5) * C(20,0) = 792 * 1 = 792
Total = 41800 + 9900 + 792 = 52492
Therefore, there are 52492 possible committees with at least three women.