Question

There are 4 Board of Directors positions open. 2 will be for men, 2 will be for women.

Out of 20 candidates, 11 are men, 9 are women. How many total outcomes are
possible?

Answer 1

4290

Explanation:

Lets find the total number of men and women .

9 women are out and 2 became the member of the Board=> total 11 women

11 men are out and 2 became the member of the Board=> total 13 men

11 women-candidates for 2 positions can make C11 2 outcomes =11!/(11-2)!/2

13 men-candidates for 2 positions can make C13 2 outcomes= 13!/(13-2)!/2

The total number of outcomes is C11 2 *C13 2 = 13!*11!/9!/11!/2/2=

10*11*12*13/2/2=11*13*5*6=4290 outcomes