Using the permutation formula, it is found that the people can be chosen for the roles in 6840 ways.
The order in which the people are chosen is important, as there are different roles, hence 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, 3 people will be chosen from a set of 20 people, hence the number of ways is given by:
[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]
More can be learned about the permutation formula at https://brainly.com/question/25925367
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