Okay,so: Assume that there are 8 unfilled roles:

Question

3 male and 5 female. There are 5 men and 6 women, including Sally, auditioning for a part in the play.

How many of these casts include Sally?

Answer 1

since Sally has to be chosen, we need 4 more females from the 5 remaining females, and 3 of the 5 men

number of casts with Sally
= 1*C(5,4) * C(5,3)
= 1*5*10 = 50