Question

At a certain high school, the Prom Committee is going to choose new members. There are 7 students from the Junior class and 10 students from the Senior class who are willing to be new members. In how many ways can 8 new members be chosen if more than 5 must be from the Senior class?

Answer 1

We have:

7 students from the junior class

10 students from the senior class

So:

We need 5 from the senior class

There are a total of 17 students so. the ones that can be any grade are:

$17-6=11$

since you need a total of 8 students in the committee and 5 have to be in the categories described above, that leaves:

$8-6=2$

That can be any grade.

Therefore:

$C(8,6)*C(11,2)=28*55=1540$

Where the combination formula is given by:

$C(n,k)=nCk=\frac{n!}{k!(n-k)!}$