For this problem, assume 7 males audition, one of them being Miles, 5 females audition, one of them being Margaret, and 6 children audition.

Question

The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

 

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

 

 

THE ANSWER IS NOT 360!

Answer 1

This is a combination and counting problem where you use combinations to find the number of possible men, women and children and multiply the three numbers together. Given that Miles and Margaret are chosen, that means C(6,2)*C(1,1)*C(6,2)

 

Note here that there is only one female role available here and Margaret has taken it.

 

Hope that helps!