/*! 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} Q22 In Exercises 5鈥�36, express all... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q22 (page 175)

In Exercises 5鈥�36, express all probabilities as fractions.

Classic Counting Problem A classic counting problem is to determine the number of different ways that the letters of 鈥淢ississippi鈥� can be arranged. Find that number.

Short Answer

Expert verified

The number of different (unique) ways in which the letters of the word 鈥淢ississippi鈥� can be arranged is 34650.

Step by step solution

01

Given information

The letters of the word 鈥淢ississippi鈥� have to be arranged.

02

Permutation in the case of repetition of letters

Several different permutations/arrangements can be made for n units if n1 are of one type, n2 are of another type, and so on.

n!n1!脳n2!脳...

03

Compute the number of ways different arrangements for the letters

The total number of letters (n) is 11.

The number of times the letter 鈥渋鈥� is repeated is 4.

The number of times the letter 鈥渟鈥� is repeated is 4.

The number of times the letter 鈥減鈥� is repeated is 2.

The total number of permutations possible to arrange the letters of the word 鈥淢ississippi鈥� is given as follows:

11!4!脳4!脳2!=11脳10脳9脳8脳7脳6脳5脳4!4!脳4脳3脳2脳1脳2脳1=34650

Therefore, the number of different ways in which the letters of the word 鈥淢ississippi鈥� can be arranged is 34650.

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

Complements and the Addition Rule Refer to the table used for Exercises 9鈥�20. Assume that one order is randomly selected. Let A represent the event of getting an order from McDonald鈥檚 and let B represent the event of getting an order from Burger King. Find PAorB炉, find PA炉orB炉, and then compare the results. In general, does PAorB炉= PA炉orB炉?

Denomination Effect. In Exercises 13鈥�16, use the data in the following table. In an experiment to study the effects of using four quarters or a \(1 bill, college students were given either four quarters or a \)1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from 鈥淭he Denomination Effect,鈥� by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Purchased Gum

Kept the Money

Students Given Four Quarters

27

46

Students Given a $1 bill

12

34

Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

c. What do the preceding results suggest?

Probability from a Sample Space. In Exercises 33鈥�36, use the given sample space or construct the required sample space to find the indicated probability.

Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2 on page 135): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

At Least One. In Exercises 5鈥�12, find the probability.

Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.

Interpreting Weather While this exercise was being created, Weather.com indicated that there was a 60% chance of rain for the author鈥檚 home region. Based on that report, which of the following is the most reasonable interpretation?

a. 60% of the author鈥檚 region will get rain today.

b. In the author鈥檚 region, it will rain for 60% of the day.

c. There is a 0.60 probability that it will rain somewhere in the author鈥檚 region at some point during the day.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.