Statistics with discrete mathAn upper-level math class has 13 students: 4 of them are females....

Step 1
13 students composed of 9 males, 4 females.
4 females composed of 2 on campus, 2 off campus.
9 males composed of 5 on campus, 4 off campus.
13 students composes of 7 on campus, 6 off campus.
Let's find the amount of groups that have two on campus members.
You need to pick 2 of the 7, so $(\genfrac{}{}{0ex}{}{7}{2})$. Then you need one more from off campus, so $(\genfrac{}{}{0ex}{}{6}{1})$
Step 2
So the number of groups with two on campus members is
$(\genfrac{}{}{0ex}{}{7}{2})(\genfrac{}{}{0ex}{}{6}{1})=126$
Now you need at least one female. So let's find all of the groups of 2 on campus members and no females, then eliminate that from the above group.
You need to pick 2 on campus males. There are 5 to choose from, so $(\genfrac{}{}{0ex}{}{5}{2})$. Then you need one from off campus, so $(\genfrac{}{}{0ex}{}{4}{1})$, giving you
$(\genfrac{}{}{0ex}{}{5}{2})(\genfrac{}{}{0ex}{}{4}{1})=40$
$126-40=86$