Question

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?

Answer 1

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

Answer 2

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.