Assume 11 males audition, one of them being Winston, 5 females audition, one of them being...
Assume 11 males audition, one of them being Winston, 5 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.
How many different ways can these roles be filled if exactly one of Winston and Margaret gets a part?
What is the probability (if the roles are filled at random) of both Winston and Margaret getting a part?
Homework Answers
a) Number of ways these roles will be filled if exactly one of Winston and Margaret gets a part = Number of ways these roles will be filled if Winston gets a part + Number of ways these roles will be filled if Margaret gets a part
= 10C2 * 4C1 * 4C2 + 10C3 * 1 * 4C2
= 45 * 4 * 6 + 120 * 1 * 6
= 1800
b) Total number of ways to fill the roles = 11C3 * 5C1 * 4C2 = 165 * 5 * 6 = 4950
P(both Winston and Margaret getting a part) = 10C2 * 1 * 4C2 / 4950 = 45 * 1 * 6 / 4950 = 0.0545
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