/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 In a production of West Side Sto... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 46

In a production of West Side Story, eight actors are considered for the male roles of Tony, Riff, and Bernardo. In how many ways can the director cast the male roles?

Short Answer

Expert verified
The director can cast the roles in 336 different ways.

Step by step solution

01

Understand the Problem

In this problem, there are 8 actors and 3 roles to be filled, namely Tony, Riff, and Bernardo. Each actor can only take one part and one part can only be played by one actor. Therefore, this is a case of permutations.
02

Calculate Permutations

Permutations are calculated using the formula \( P(n, r) = \frac{n!}{(n-r)!} \) where \( n \) is the total number of possibilities, \( r \) is the number of possibilities chosen, and \( ! \) denotes a factorial, meaning the product of all positive integers up to that number. Substituting \( n = 8 \) and \( r = 3 \) into the formula, you get \( P(8, 3) = \frac{8!}{(8-3)!} \).
03

Solve the Factorials

Solve for the factorials in the formula. \( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \) and \( (8-3)! = 5! = 5 \times 4 \times 3 \times 2 \times 1 \). Substitute those values back into the formula: \( P(8, 3) = \frac{40320}{120} \).
04

Final Calculation

Divide \( 40320 \) by \( 120 \) to get the number of different ways the three roles can be cast by the eight actors. So the final answer is \( P(8, 3) = 336 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The tables in Exercises 3-4 show claims and their probabilities for an insurance company. a. Calculate the expected value and describe what this means in practical terms. b. How much should the company charge as an average premium so that it breaks even on its claim costs? c. How much should the company charge to make a profit of \(\$ 50\) per policy? PROBABILITIES FOR MEDICAL INSURANCE CLAIMS $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Amount of Claim (to the } \\ \text { nearest } \mathbf{\$ 2 0 , 0 0 0 )} \end{array} & \text { Probability } \\ \hline \$ 0 & 0.70 \\ \hline \$ 20,000 & 0.20 \\ \hline \$ 40,000 & 0.06 \\ \hline \$ 60,000 & 0.02 \\ \hline \$ 80,000 & 0.01 \\ \hline \$ 100,000 & 0.01 \\ \hline \end{array} $$

A person can order a new car with a choice of six possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?

Consider a political discussion group consisting of 5 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting two Republicans.

In a product liability case, a company can settle out of court for a loss of \(\$ 350,000\), or go to trial, losing \(\$ 700,000\) if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdict to be \(0.8\). a. Find the expected value of the amount the company can lose by taking the case to court. b. Should the company settle out of court?

In Exercises 43-48, an ice chest contains six cans of apple juice, eight cans of grape juice, four cans of orange juice, and two cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of apple juice.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.