Peyton Velez

2022-06-24

In my textbook MP is strictly reserved to counting lists. Does what I do below to count subsets work?
Consider 3 men(Ace, Bob, Corry) and 3 women(Ann, Beth, Candace). Suppose we need to choose a team with 2 men and 2 women in it. An example team is $\left\{\text{Ace, Ann, Beth, Bob}\right\}$ which is the union of $\left\{\text{Ace, Bob}\right\}\left\{\text{Beth, Ann}\right\}.$ So we simply count 2−lists whose first element is a set of two men and whose second element is a set of two women. We get the same number of 2−lists if their first element is a set of two women. There are $\left(\genfrac{}{}{0}{}{3}{2}\right)=8$ two-men subsets and that many two-women subsets. So there are 8 choices for the first element and 8 choices for the second one. In all there are ${8}^{2}={\left(\genfrac{}{}{0}{}{3}{2}\right)}^{2}=64$ two element lists = teams with two men and two women in each.

Marlee Guerra

Expert

it's all good except $\left(\genfrac{}{}{0}{}{3}{2}\right)=3$ (not 8) so the true answer should be 9.