5 Roles; 10 People Audition; How Many Combinations?

Question

The drama teacher at your high school is holding auditions for a small play with only 5 roles. If ten people try out, how many different ways can the roles be assigned?

Answer 1

Assuming that a person only plays one role, would the total number of combinations not be "n choose 5" = C(n,k)  = n!/((n-k)!*k!)?