Answer: You have to think about permutations
Explanation:
There are five main roles to be filled, and 15 people auditioning for them. To calculate the number of ways to fill the roles, we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of people auditioning, and r is the number of roles to be filled.
For the first role (Belle), there are 15 options. For the second role (Beast), there are 14 options remaining, since one person has already been chosen for Belle. For the third role (Gaston), there are 13 options remaining, and so on.
Using the permutation formula, we can calculate the total number of ways to fill the roles as:
15P5 = 15! / (15 - 5)!
= 15! / 10!
= 15 x 14 x 13 x 12 x 11
= 360,360
Therefore, there are 360,360 different ways to fill the roles in the production of Beauty and the Beast with 15 people auditioning for the roles.