Question

You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.


A: If no one has been cast yet, how many different ways are there to cast Fantine from the 28 women?


B: If Fantine has already been cast, how many different ways are there to cast adult Cosette from the remaining women?


C: If Fantine and adult Cosette have already been cast, how many different ways are there to cast Éponine from the remaining women?


Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.


B: 27P2

C: 26

C: 26!

A: 28P3

B: 27

C: 26P1

A: 28

B: 27!

A: 28!

Question 2:
A: Which of the following expressions will calculate the number of ways the three lead female roles could be cast?

B: Evaluate the permutation from part A.

Select one answer choice for part A, and one answer choice for part B.

B: ≈3.05×10^29
A: 28P3
B: 19656
A: 3P28
B: ≈5.08×10^28
A: 28P25

Answer 1

The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.

How to calculate the value?

The different ways that are there to cast Fantine from the 28 women will be:

= 28!/(28 - 1)!

= 28!/27!

= 28

When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:

= 27!(27 - 1)!

= 27!/26!

= 26

When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:

= (28 - 2)!/(28 - 2 - 1)!

= 26!/25!

= 25

Learn more about permutations on:

brainly.com/question/4658834

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