A theater company with 9 actors is putting on a play that has 3 roles. In how many different ways can the director assign actors to those roles?

Question

Mathematics

Nugget

12 May, 19:28

A theater company with 9 actors is putting on a play that has 3 roles. In how many different ways can the director assign actors to those roles?

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Answers (2)

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Ada Rogers · Answer 1

He has 9 choices for the first role, and that leaves him 8 people to choose for the second so he has 9*8 = 72 choices for the first two roles; that leaves 7 possible choices for the third role so that gives him 9*8*7 choices or 504 different ways he can assign the roles. i think this is correct.

Headlights · Answer 2

9! / (3!*6!) = 7*8*9/6=84