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- #1

For this problem, assume 10 males audition, one of them being Dale, 7 females audition, one of them being Margaret, and 4 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

1) How many different ways can these roles be filled if exactly one of Dale and Margaret gets a part?

2) What is the probability (if the roles are filled at random) of both Dale and Margaret getting a part?

For number 1, I have tried these permutations and none have worked:

Dale but not Margaret, P(9,2)P(6,1)P(4,2) + Margaret but not Dale, P(9,3)(1)P(4,2)

Dale, P(9,2)P(7,1)P(4,2) + Margaret, P(10,3)P(1)P(4,2) - Both Dale and Margaret,P(9,2)(1)P(4,2)

I also tried both by multiplying P(3,1) to denote the 3 roles Dale could get, but that did not work either.