Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134506470
Author: Pirnot
Publisher: PEARSON
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Chapter 12.CT, Problem 4CT
Use the sixth row of Pascal’s triangle to find the number of three-element subsets that can be chosen from a six-element set.
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In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a
random sample of 1014 adults aged 18 and over. One of the questions was, "How many
cups of coffee, if any, do you drink on an average day?" The following table shows the
results obtained (Gallup website, August 6, 2012).
Number of Cups
per Day
0
1
2
3
4 or more
Number of
Responses
365
264
193
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let
x=4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an
average day. For this group, let y = the number of cups of coffee consumed on an
average day. Compute the expected value of y and compare it to the expected value of x.
Ten major college football bowl games were played in January 2010, with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the 10 bowl games follow (USA Today, January 8, 2010).
Bowl Game
Score
Outback
Gator
Auburn 38 Northwestern 35
Florida State 33 West Virginia 21
Capital One
Penn State 19 LSU 17
Rose
Ohio State 26 Oregon 17
Florida 51 Cincinnati 24
Sugar
Cotton
Alamo
Fiesta
Mississippi State 21 Oklahoma State 7
Texas Tech 41 Michigan State 31
Boise State 17 TCU 10
Orange
Iowa 24 Georgia Tech 14
Championship
Alabama 37 Texas 21
Predicted
Point Margin
Actual
Point Margin
5
3
1
12
3
-2
14
3
9
-4
-3
4
229740706
14
10
10
16
The predicted winning point margin was based on Las Vegas betting odds approximately
one week before the bowl games were played. For example, Auburn was predicted to beat
Northwestern in the Outback Bowl by five points. The actual winning point margin for Au-
burn was three points. A…
Chapter 12 Solutions
Mathematics All Around (6th Edition)
Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - How many different two-digit numbers can you form...Ch. 12.1 - How many different two-digit numbers can you form...
Ch. 12.1 - How many different three-digit numbers can you...Ch. 12.1 - How many different three-digit numbers can you...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - In Exercises 1318, assume you are rolling two...Ch. 12.1 - Recall in Example 6 that you are creating outfits...Ch. 12.1 - Recall in Example 6 that you are creating outfits...Ch. 12.1 - Use the given diagram to solve Exercises 21 and...Ch. 12.1 - Use the given diagram to solve Exercises 21 and...Ch. 12.1 - Answer Exercise 21 assuming the diagram has six...Ch. 12.1 - Prob. 24ECh. 12.1 - Assigning tasks. Stefans friends Amika, Pam, Li,...Ch. 12.1 - Making staff assignments. Suppose that the staff...Ch. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - The role-playing game Dungeons & Dragons uses a...Ch. 12.1 - Dungeons & Dragons also uses 12-sided dice. How...Ch. 12.1 - Counting license plates. An eyewitness to a crime...Ch. 12.1 - Counting license plates. In a small state, the...Ch. 12.1 - For Exercises 33 and 34, use the figures below....Ch. 12.1 - For Exercises 33 and 34, use the figures below....Ch. 12.1 - Prince William and Duchess Kate are attending the...Ch. 12.1 - Prince William and Duchess Kate are attending the...Ch. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Stacking cans. In preparation for Thanksgiving...Ch. 12.1 - Prob. 40ECh. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - In Exercises 4144, you are buying a triple-deck...Ch. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.2 - Assigning responsibilities. The board of an...Ch. 12.2 - Assigning positions. If there are 12 members on...Ch. 12.2 - Assigning officers. The Equestrian Club has eight...Ch. 12.2 - Assigning officers. If the Chamber of Commerce has...Ch. 12.2 - Choosing a stand up paddle board package. Kevin...Ch. 12.2 - Counting schedules. Jorge is using his educational...Ch. 12.2 - Counting meal possibilities. The early bird...Ch. 12.2 - Prob. 8ECh. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In games such as Dungeons 12, determine the number...Ch. 12.2 - In Exercises 1316, using the digits 0,1,2,...,8,9,...Ch. 12.2 - In Exercises 1316, using the digits 0,1,2,...,8,9,...Ch. 12.2 - In Exercises 1316, using the digits 0,1,2,...,8,9,...Ch. 12.2 - Prob. 16ECh. 12.2 - A truefalse quiz. In how many ways can you choose...Ch. 12.2 - A multiple-choice test. In how many ways can you...Ch. 12.2 - Planning a trip. Center City Community Colleges...Ch. 12.2 - A piano competition. In the Van Cliburn piano...Ch. 12.2 - Enumerating call letters. Radio stations in the...Ch. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Counting license plates. In a certain state,...Ch. 12.2 - A pin tumbler lock has a series of pins, each of...Ch. 12.2 - A pin tumbler lock has a series of pins, each of...Ch. 12.2 - Counting routes for an armored van. A Wells Fargo...Ch. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Facial arrangements. A website enables you to...Ch. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Exercises 33 and 34 are alternative versions of...Ch. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Assume that we wish to seat three men and three...Ch. 12.2 - Assume that we wish to seat three men and three...Ch. 12.2 - Assume that we wish to seat three men and three...Ch. 12.2 - In solving counting problems, it is often useful...Ch. 12.2 - What is the relationship between trees, slot...Ch. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.3 - In Exercises 112, calculate each value. 4!Ch. 12.3 - Prob. 2ECh. 12.3 - In Exercises 112, calculate each value. (85)!Ch. 12.3 - In Exercises 112, calculate each value. (105)!Ch. 12.3 - In Exercises 112, calculate each value. 107Ch. 12.3 - In Exercises 112, calculate each value. 119Ch. 12.3 - Prob. 7ECh. 12.3 - In Exercises 112, calculate each value. 1192Ch. 12.3 - In Exercises 112, calculate each value. P(6,2)Ch. 12.3 - In Exercises 112, calculate each value. P(5,3)Ch. 12.3 - In Exercises 112, calculate each value. C(10,3)Ch. 12.3 - In Exercises 112, calculate each value. C(4,4)Ch. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1518 find the number of permutations....Ch. 12.3 - In Exercises 1922, find the number of...Ch. 12.3 - Prob. 20ECh. 12.3 - In Exercises 1922, find the number of...Ch. 12.3 - Prob. 22ECh. 12.3 - Find the eighth row in Pascals triangle.Ch. 12.3 - Find the tenth row in Pascals triangle.Ch. 12.3 - Use the seventh row of Pascals triangle to answer...Ch. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - In Exercises 2730, describe where each number is...Ch. 12.3 - Prob. 29ECh. 12.3 - In Exercises 2730, describe where each number is...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 32ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 34ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - Prob. 42ECh. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 3144, specify the number of ways to...Ch. 12.3 - In Exercises 4548, determine the number of ways to...Ch. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - In Exercise 49 and 50, determine why the given...Ch. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - A typical bingo card is shown in the figure. The...Ch. 12.3 - Prob. 53ECh. 12.3 - A typical bingo card is shown in the figure. The...Ch. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - Prob. 62ECh. 12.3 - Prob. 63ECh. 12.3 - Prob. 64ECh. 12.3 - In Exercise 5568, use the fundamental counting...Ch. 12.3 - Prob. 66ECh. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Prob. 69ECh. 12.3 - Prob. 70ECh. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Prob. 73ECh. 12.3 - Prob. 74ECh. 12.3 - Prob. 75ECh. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Prob. 78ECh. 12.3 - Prob. 79ECh. 12.3 - Prob. 80ECh. 12.3 - Prob. 81ECh. 12.3 - Prob. 82ECh. 12.3 - Prob. 83ECh. 12.3 - Prob. 84ECh. 12.3 - Prob. 85ECh. 12.3 - Prob. 86ECh. 12.3 - Prob. 87ECh. 12.3 - Prob. 88ECh. 12.3 - Prob. 89ECh. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Prob. 5ECh. 12.4 - Exercises 16 are based on the slot machine shown...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Prob. 9ECh. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Exercises 712 deal with the poker hands described...Ch. 12.4 - Prob. 13ECh. 12.4 - Why are we using combinations rather than...Ch. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Playing poker. How many poker hands are less in...Ch. 12.CR - Prob. 1CRCh. 12.CR - The game Dungeons & Dragons uses a tetrahedral die...Ch. 12.CR - Prob. 3CRCh. 12.CR - Prob. 4CRCh. 12.CR - Prob. 5CRCh. 12.CR - Prob. 6CRCh. 12.CR - Prob. 7CRCh. 12.CR - Prob. 8CRCh. 12.CR - Prob. 9CRCh. 12.CR - Prob. 10CRCh. 12.CR - You are going to serve gourmet cupcakes at your...Ch. 12.CR - Prob. 12CRCh. 12.CR - Prob. 13CRCh. 12.CR - Prob. 14CRCh. 12.CR - Prob. 15CRCh. 12.CR - Prob. 16CRCh. 12.CR - Prob. 17CRCh. 12.CT - List all the ways you can select two different...Ch. 12.CT - Prob. 2CTCh. 12.CT - Prob. 3CTCh. 12.CT - Use the sixth row of Pascals triangle to find the...Ch. 12.CT - Prob. 5CTCh. 12.CT - Prob. 6CTCh. 12.CT - Prob. 7CTCh. 12.CT - Prob. 8CTCh. 12.CT - Prob. 9CTCh. 12.CT - Prob. 10CTCh. 12.CT - Prob. 11CTCh. 12.CT - Prob. 12CTCh. 12.CT - Write an equation that relates the expressions...Ch. 12.CT - Prob. 14CTCh. 12.CT - Prob. 15CTCh. 12.CT - Prob. 16CT
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