How would I solve this theatre-related permutations problem?

Question

A theatre company is casting seven roles for a play that has four males and three females. If 10 men and 8 women audition, how many ways can the director cast the play? (the roles are all different)?

This problem has given me trouble because i'm not sure what every role being different means to me solving the problem.

I thought it would be 10p4 + 8p3 but he answer looks a little too low to me considering some of the other problems I've done with so many people/spots involved.

parsiad · Answer 1 · 2015-09-20T23:39:42.497

1

Hint: Are you sure you should be adding those numbers?

edited Sep 20 '15 at 23:39

answered Sep 20 '15 at 22:46

parsiad

25,154

3

It would seem that i must multiply them... – Mark Gregg Sep 20 '15 at 23:00
Correct (make sure to understand why that is the case) – parsiad Sep 20 '15 at 23:29
1

@par The notation $nPk$ or $P(n, k)$ is the number of permutations of $k$ elements selected from $n$ elements. $P(n, k) = \frac{n!}{(n - k)!}$. – N. F. Taussig Sep 20 '15 at 23:32
Ah, of course, the roles in the play are distinct. Thanks. – parsiad Sep 20 '15 at 23:39

How would I solve this theatre-related permutations problem?

1 Answers1