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There are 9 different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?
Answer:

There are $9$ different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast? $\newline$ Answer:

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Counting principle

Full solution

Q. There are

9

different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?

\newline

Answer:

Determine Number of Choices: Determine the number of ways to cast the role of Larry. $\newline$ Since there are $9$ actors to choose from for the role of Larry, there are $9$ possible choices.
Cast Role of Curly: Determine the number of ways to cast the role of Curly after Larry has been cast. $\newline$ Once Larry has been cast, there are $8$ remaining actors to choose from for the role of Curly.
Cast Role of Moe: Determine the number of ways to cast the role of Moe after Larry and Curly have been cast. $\newline$ After casting Larry and Curly, there are $7$ actors left for the role of Moe.
Calculate Total Number: Calculate the total number of ways to cast all three roles. $\newline$ The total number of ways to cast the roles is the product of the number of choices for each role. $\newline$ Total number of ways $=$ Number of choices for Larry $\times$ Number of choices for Curly $\times$ Number of choices for Moe $\newline$ Total number of ways $= 9 \times 8 \times 7$
Perform Multiplication: Perform the multiplication to find the final answer. $\newline$ Total number of ways = $9 \times 8 \times 7 = 72 \times 7 = 504$

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