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Chapter 4: Q22 (page 175)

In Exercises 5–36, express all probabilities as fractions.

Classic Counting Problem A classic counting problem is to determine the number of different ways that the letters of “Mississippi” can be arranged. Find that number.

Short Answer

Expert verified

The number of different (unique) ways in which the letters of the word “Mississippi” can be arranged is 34650.

Step by step solution

01

Given information

The letters of the word “Mississippi” 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!×n2!×...

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 “i” is repeated is 4.

The number of times the letter “s” is repeated is 4.

The number of times the letter “p” is repeated is 2.

The total number of permutations possible to arrange the letters of the word “Mississippi” is given as follows:

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

Therefore, the number of different ways in which the letters of the word “Mississippi” can be arranged is 34650.

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Most popular questions from this chapter

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana: Use If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana?

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

At Least One Correct Answer If you make random guesses for 10 multiple choice SAT test questions (each with five possible answers), what is the probability of getting at least 1 correct? If these questions are part of a practice test and an instructor says that you must get at least one correct answer before continuing, is there a good chance you will continue?

In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

McDonald’s

Burger King

Wendy’s

Taco Bell

Order Accurate

329

264

249

145

OrderNotAccurate

33

54

31

13

Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order from Burger King or Taco Bell or an order that is accurate.

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Job Applicant Mistakes Based on an Adecco survey of hiring managers who were asked to identify the biggest mistakes that job candidates make during an interview, there is a 50–50 chance that they will identify “inappropriate attire.”

Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using a \(1 bill or a \)1 bill, college students were given either a \(1 bill or a \)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 “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Purchased Gum

Kept the Money

Students Given A \(1 bill

27

46

Students Given a \)1 bill

12

34

Denomination Effect

a. Find the probability of randomly selecting a student who kept 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 a $1 bill.

c. What do the preceding results suggest?
See all solutions

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