Jon P. answered • 02/18/15

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You have to figure the number of way to assign the male roles and female roles separately and then multiply to find the total number of casts.

So, with 6 men and 3 male roles, there are 6! / (3! (6-3)!) = 6! / (3!3!) = 20 different ways to assign the male roles.

Similarly there are 9! / (5! (9-5!)) = 9! / (5!4!) = 126 different ways to assign the female roles.

So there are 20*126 = 2520 different casts.

To find how many casts include Sally, assume that she has one of the roles and then find the number of ways to assign the other 4 female roles to the other 8 women. That's 8! / ((4!) (8-4)!) = 8! / (4!4!) = 70. So multiply that by the number of ways to assign the male roles (20) to get 1400 different casts that include Sally.