Part 1

You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production ofLes Misrablesthis 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 ponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from28women and22men who are interested in auditioning for these parts.

Question 1:

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 ponine from the remaining women?

Select one answer choice for partA, one answer choice for partB, and one answer choice for partC.

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 partA, and one answer choice for partB.

B:3.0510^29

A:28P3

B:19656

A:3P28

B:5.0810^28

A:28P25

Question 3:

A:If no one has been cast yet, how many different ways are there to cast Jean Valjean from the22men?

B:If Jean Valjean has already been cast, how many different ways are there to cast Inspector Javert from the remaining men?

C:If Jean Valjean and Inspector Javert have already been cast, how many different ways are there to cast Marius from the remaining men?

Select one answer choice for partA, one answer choice for partB, and one answer choice for partC.

A:22P3

A:22!

B:21!

C:20P1

B:21

B:21P2

C:20!

A:22

C:20

Question 4

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

B:Evaluate the permutation from partA.

Select one answer choice for partA, and one answer choice for partB

A:22P19

B:1.1210^21

B:9240

A:3P22

A:22P3

B:1.8710^20

Part 2

You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production ofLes Misrablesthis year, and they need your help planning it.

All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thnardier, Enjolras, Marius, Fantine, adult Cosette, adult ponine, and Madame Thnardier. It is your job to seat these9actors, the3producers, and the director around the table.

Question 1:

If the9actors must sit together, how many ways are there to seat the13people around the table?

8,709,120

362,880

6,227,020,800

259,459,200

Question 2:

Remember that there are5lead male roles and4lead female roles. If you must seat the male leads together, the female leads together, the3producers together, and the director by himself, how many different ways can you seat the13people around the circular table?

103,680

479,001,600

6,227,020,800

17,280

Question 3:

InLes Misrables, Monsieur Thnardier and Madame Thnardier are married, and during Act 2, Cosette and Marius become married. If the Thnardiers must next to one another, and Cosette and Marius must sit next to one another,but there are no restrictions on how the others can sit, how many different ways can you seat the13people around the circular table?

4

17,160

14,515,200

6,227,020,800