Question

For this problem, assume 8 males audition, one of them being Alessandro, 4 females audition, one of them being Ramatou, and 5 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

(1) How many different ways can these roles be filled from these auditioners?

(2) How many different ways can these roles be filled if exactly one of Alessandro and Ramatou gets a part?

(3) What is the probability (if the roles are filled at random) of both Alessandro and Ramatou getting a part?

Answer 1

(1) Number of ways in which the roles can be filled = 8C5 x 4C1 x 5C2

= 56x4x10

= 2240

(2) Number of ways in which these roles be filled if exactly one of Alessandro and Ramatou gets a part = Number of ways in which these roles be filled if only Alessandro gets a part + Number of ways in which these roles be filled if only Ramatou gets a part

= 1 x 7C2 x 3C1 x 5C2 + 8C3 x 1 x 5C2

= 21x3x10 + 56x1x10

= 630 + 560

= 1190

(3) P(both Alessandro and Ramatou getting a part) = 1x7C2x1x5C2 / 2240

= 210/2240

= 0.09375