For this problem, assume 11 males audition, one of them being Miles, 5 females audition, one of them being Barbara, and 6 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?

answer: 148500

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

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