In a production of west side story, eight actors are considered for the male roles of Tony, Riff, and Bernardo.

Question

a.) is this permutation or combination?
b.) in how many ways can the director cast the male roles?

Answer 1

If the roles can be changed among the three selected actors, then it is a combination. If they cannot, then it is a permutation.

Therefore a permutation is usually a bigger number than a combination, because to get the combination, we divide the permutation by the number of arrangements of the selected candidates.

Permutation: P(n,r)=n!/(n-r)!
Combination: C(n,r)=n!/((n-r!)r!)

Answer 2

b.) 8P3 = 336