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

1980 total outcomes are possible.

Explanation:

The order in which the candidates are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

How many total outcomes are possible?

2 men, from a set of 11.

2 women, from a set of 9.

So

`T = C_(11,2)*C_(9,2) = (11!)/(2!9!)*(9!)/(2!7!) = 1980`

1980 total outcomes are possible.