How many of these casts include Sally?

Question

 Assume that there are 8 unfilled roles: 4 male and 4 female. There are 5 men and 6 women, including Sally, auditioning for a part in the play.

Answer 1

Solution1:

So let's select Sally, because she must be selected. We now have a pool of 5 males and 5 females, from which we need 4 males and 3 females (Sally is already selected). This can be done in C(5,4)*C5,3)= 5*10=50 different ways.

50 different options will include Sally.

Solution#2

There are a total of C(5,4)*C6,4)= 5* 15= 75 ways to select 4 men and 4 women.

The number of ways we do not select Sally : C(5,4)*C(5,4)= 5*5 = 25

Therefore the number of ways we select Sally in this case is 75 - 25 = 50 (Same answer as in option1