There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible? a. 120 b. 720 c. 1,060 d. 1,520 e. 1,980
Mathematics · High School · Wed Jan 13 2021
llm
Answered on
Given :
Number of women = 11
Number of men = 9
Number of women to be selected in committe = 2
Number of men to be selected in committe = 2
Formula :
nCr = n!/r!(n-r)!
11C2 = 11!/2!(11-2)!
= 11 × 10 × 9!/2 × 9!
= 55
And,
9C2 = 9!/2!(9-2)!
= 9 × 8 × 7!/2 × 7!
= 36
So, Number of committe of 2 men and 2 women that can be formed from 9 men and 11 women = 55 × 36
= 1980