/*! 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 40 In how many ways can six people ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 40

In how many ways can six people sit in a six-passenger car?

Short Answer

Expert verified
There are 720 ways for six people to sit in a six-passenger car.

Step by step solution

01

Understanding the concept of permutations

A permutation is an arrangement of objects, without repetition, in a specific order. Since we are arranging people in the car and the order is important (i.e., sitting in the driver's seat is different from sitting in the passenger seat etc.), this is a permutation problem. In general, the number of permutations of n objects taken r at a time is given by \( nPr = n! / (n - r)! \), where \( n! \) is the factorial of n, which is the product of all positive integers up to n.
02

Applying the formula to our problem

In this scenario, both n and r are equal to 6, as we have six people and six seats. Hence, we need to calculate \( 6P6 \), which equals \( 6! / (6 - 6)! = 6! / 0! \). Any non-zero number's factorial is the product of all positive numbers less than or equal to that number, and \( 0! \) is defined as 1.
03

Calculating the answer

\( 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720 \), and since \(0! = 1\), we have \(6P6 = 6! / 0! = 720 / 1 = 720\).

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

In Exercises 1 - 7, fill in the blanks. To determine the ________ of an event, you can use the formula \( P\left(e\right) = \dfrac{n\left(E\right)}{n\left(S\right)} \), where \( n\left(E\right) \) is the number of outcomes in the event and \( n\left(S\right) \) is the number of outcomes in the sample space.

In Exercises 25 - 30, find the probability for the experiment of tossing a six-sided die twice. The sum is \( 2 \), \( 3 \), or \( 12 \).

In Exercises 39 - 42, you are given the probability that an event will not happen. Find the probability that the event will happen. \( P(E') = \dfrac{17}{35} \)

Assume that the probability of the birth of a child of a particular sex is \( 50\% \). In a family with four children, what are the probabilities that(a) all the children are boys, (b) all the children are the same sex, and (c) there is at least one boy?

In Exercises 39 - 42, you are given the probability that an event will not happen. Find the probability that the event will happen. \( P(E') = 0.23 \)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.