Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.
There are different roles, hence the order is important, which means that the permutation formula is used.
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:
[tex]P_{17,4} = \frac{17!}{13!} = 57120[/tex].
More can be learned about the permutation formula at https://brainly.com/question/25925367
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