If there are $5$ women and $5$ men, how many possibilities exist to form a committee of $3$ women and $2$ men.

Question

I just wish to confirm if my understanding is correct for the following problem:

If there are $5$ women and $5$ men, how many possibilities exist to form a committee of $3$ women and $2$ men.

So I have computed this problem as below:

$\binom{5}{3} \times\binom{5}{2} = 100$possibilities.

Is this correct?

Answer 1

Yes. $\binom{5}{3} \times \binom{5}{2} = 100$ is correct.