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Sam is making a short film. There are $4$ leading actors and $5$ leading actresses to choose from. How many different ways can Sam cast this short film? $\newline$ _____ short films

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Counting principle

Full solution

Q. Sam is making a short film. There are

4

leading actors and

5

leading actresses to choose from. How many different ways can Sam cast this short film?

\newline

_____ short films

Identify Choices: Identify the number of choices for each role. Sam needs to choose one leading actor and one leading actress for the short film. $\newline$ Number of choices for leading actor = $4$ $\newline$ Number of choices for leading actress = $5$
Apply Counting Principle: Apply the Basic Counting Principle. The number of different ways to cast the short film is the product of the number of choices for the leading actor and the number of choices for the leading actress. $\newline$ Total number of ways to cast the short film $= \text{Number of choices for leading actor} \times \text{Number of choices for leading actress}$ $\newline$ Total number of ways to cast the short film $= 4 \times 5$
Perform Calculation: Perform the calculation to find the total number of different ways to cast the short film. $\newline$ Total number of ways to cast the short film = $4 \times 5 = 20$

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