Assume that there are 6 unfilled roles:
3 male and 3 female. There are 4 men and 4 women, including
Jennifer, auditioning for a part in the play.


(1) How many different casts are there?




(2) How many of these casts include Jennifer?

This has to do with permutations and combinations.

If you have to choose m people for n roles, the number of ways this can be done is given by mCn, or:

\frac{m(m-1)(m-2)...(m-n)}{(1)(2)(3)...(n)}

Can you give your problem a try?