The number of different casts possible is the number of permutations of 16 female actors and 9 male actors for the 15 speaking roles. This can be calculated using the formula:
P(16, 10) x P(9, 5) = 16!/(16-10)! x 9!/(9-5)! = 16!/(6! x 9!/(4! = 16!/(6! x 4!) = 16!/(24 x 4!) = 16!/(96) = 16,796,160
A play contains 15 speaking roles, 10 of them female and 5 male. If the director can choose among 16 female actors and 9 male actors to fill the roles, how many different casts are possible? (NOTE: A cast includes BOTH the actor AND the role that they play.)
I'm just confused on how to set this up. It deals with permutations cause I know there's order, but I'm still not sure what I should be choosing from. I know that I have to multiple the female roles and male roles to get the total, but could you help me set it up? Thank you.
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