Assume that there are 6 unfilled roles: 1 male and 5 female. There are 2 men and 8 women, including Ann, auditioning for a part in the play.

Question

(1) How many different casts are there? 

(2) How many of these casts include Ann? 

Answer 1

(1) Total different casts = 2·P(8,5) = 13440

(2) Total casts with ANN = 2·P(8,5) - 2P(8,4) = 10080