Question

There are nine men and ten women in a club; in how many ways can a committee of four be formed?

Answer 1

There are 19 people total, and groups of four are being asked of us. We can use the formula for permutations or combinations.

Permutations: $\frac{n!}{(n-r)!}$
Combinations: $\frac{n!}{r!(n-r)!}$
Where in both scenarios, there are n objects being chosen at r times.

19 P 4 is 93024
19 C 4 is 3876
It all depends on whether order matters with group placement; if it does, your answer is 93024, if not, then your answer is 3876.

:)