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Chapter 11: Problem 4

In how many ways can a casting director choose a female lead and a male lead from five female actors and six male actors?

Short Answer

Expert verified
The director can choose a lead actor and actress in 30 different ways.

Step by step solution

01

Understand the Problem

The casting director needs to choose one actor from the six available male actors, and one actress from the five available female actresses. These selections are independent events.
02

Applying Permutation Formula

To select one actor from six, the number of ways the selection can be done is given by \( P(6,1) = 6 \). Similarly, to select one actress from five, we have \( P(5,1) = 5 \).
03

Apply Principle of Multiplicativity

Since these are independent events, the total number of ways of choosing a male lead and a female lead is \( 6 * 5 = 30 \).

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