College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134674148
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Chapter 7, Problem 58RE
To determine

To discuss: The validity of the statement “If n and r positive integers and 1<r<n, then Cnr<n!”. If the statement is always true, explain why. If not, give a counterexample.

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Chapter 7 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 7.1 - Consider the propositions p and q: p: “142 <...Ch. 7.1 - Prob. 2MPCh. 7.1 - Prob. 3MPCh. 7.1 - Prob. 4MPCh. 7.1 - Prob. 5MPCh. 7.1 - Prob. 6MPCh. 7.1 - Prob. 7MPCh. 7.1 - Prob. 8MPCh. 7.1 - Prob. 1EDCh. 7.1 - If a compound proposition contains three variables...
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Explain why the sum of any two odd integers is...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - In Problems 9–14, express each proposition as an...Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - In Problems 15–20, express each proposition as an...Ch. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - In Problems 21–28, describe each proposition as a...Ch. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - In Problems 21–28, describe each proposition as a...Ch. 7.1 - Prob. 27ECh. 7.1 - In Problems 21–28, describe each proposition as a...Ch. 7.1 - Prob. 29ECh. 7.1 - In Problems 29–34, state the converse and the...Ch. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - In Problems 35–52, construct a truth table for the...Ch. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - In Problems 35–52, construct a truth table for the...Ch. 7.1 - In Problems 35–52, construct a truth table for the...Ch. 7.1 - In Problems 35–52, construct a truth table for the...Ch. 7.1 - Prob. 43ECh. 7.1 - In Problems 35–52, construct a truth table for the...Ch. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - In Problems 35–52, construct a truth table for the...Ch. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - In Problems 53-58, construct a truth table to...Ch. 7.1 - In Problems 59–64, construct a truth table to...Ch. 7.1 - Prob. 60ECh. 7.1 - In Problems 59–64, construct a truth table to...Ch. 7.1 - In Problems 59–64, construct a truth table to...Ch. 7.1 - In Problems 59–64, construct a truth table to...Ch. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Let p be the proposition “every politician is...Ch. 7.1 - Prob. 71ECh. 7.1 - If the conditional proposition p is a...Ch. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.2 - Let G be the set of all numbers such that x2 =...Ch. 7.2 - Prob. 2MPCh. 7.2 - Prob. 3MPCh. 7.2 - Prob. 4MPCh. 7.2 - Prob. 5MPCh. 7.2 - Prob. 6MPCh. 7.2 - Refer to Example 7. How many customers purchased...Ch. 7.2 - Prob. 1EDCh. 7.2 - Prob. 2EDCh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - In Problems 1–6, answer yes or no. 6. If the...Ch. 7.2 - In Problems 7–14, indicate true (T) or false...Ch. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - In Problems 7–14, indicate true (T) or false...Ch. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - In Problems 15–28, write the resulting set using...Ch. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - In Problems 15–28, write the resulting set using...Ch. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - In Problems 15–28, write the resulting set using...Ch. 7.2 - In Problems 15–28, write the resulting set using...Ch. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - In Problems 15–28, write the resulting set using...Ch. 7.2 - In Problems 15–28, write the resulting set using...Ch. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - In Problems 31–44, refer to the Venn diagram below...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - In Problems 31–44, refer to the Venn diagram below...Ch. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - In Problems 31–44, refer to the Venn diagram below...Ch. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - In Problems 31–44, refer to the Venn diagram below...Ch. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - If R = {1, 3, 4} and T = {2, 4, 6}, find {x|x ∊ R...Ch. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Prob. 55ECh. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - In Problems 63–72, discuss the validity each...Ch. 7.2 - Prob. 64ECh. 7.2 - In Problems 63–72, discuss the validity of each...Ch. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.2 - Prob. 68ECh. 7.2 - Prob. 69ECh. 7.2 - Prob. 70ECh. 7.2 - Prob. 71ECh. 7.2 - Prob. 72ECh. 7.2 - Prob. 73ECh. 7.2 - Prob. 74ECh. 7.2 - Prob. 75ECh. 7.2 - Prob. 76ECh. 7.2 - Prob. 77ECh. 7.2 - Prob. 78ECh. 7.2 - Prob. 79ECh. 7.2 - Prob. 80ECh. 7.2 - Prob. 81ECh. 7.2 - Prob. 82ECh. 7.2 - Prob. 83ECh. 7.2 - Prob. 84ECh. 7.2 - Prob. 85ECh. 7.2 - Prob. 86ECh. 7.2 - Prob. 87ECh. 7.2 - Prob. 88ECh. 7.2 - Committee selection. A company president and three...Ch. 7.2 - Prob. 90ECh. 7.2 - Prob. 91ECh. 7.2 - Prob. 92ECh. 7.2 - Prob. 93ECh. 7.2 - Blood types. When receiving a blood transfusion, a...Ch. 7.2 - Prob. 95ECh. 7.2 - Prob. 96ECh. 7.2 - Prob. 97ECh. 7.2 - Prob. 98ECh. 7.3 - The survey in Example 1 also indicated that 345...Ch. 7.3 - Students at a university have the option to stream...Ch. 7.3 - Prob. 3MPCh. 7.3 - Each question on a multiple-choice test has 5...Ch. 7.3 - Prob. 5MPCh. 7.3 - Prob. 1EDCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - An entertainment guide recommends 6 restaurants...Ch. 7.3 - A college offers 2 introductory courses in...Ch. 7.3 - How many 3-letter code words can be formed from...Ch. 7.3 - How many 4-letter code words can be formed from...Ch. 7.3 - A county park system rates its 20 golf courses in...Ch. 7.3 - The 14 colleges of interest to a high school...Ch. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - Prob. 22ECh. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - In Problems 17–24, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - In Problems 25–32, use the given information to...Ch. 7.3 - Prob. 32ECh. 7.3 - In Problems 33 and 34, discuss the validity of...Ch. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - A delicatessen serves meat sandwiches with the...Ch. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - A combination lock has 5 wheels, each labeled with...Ch. 7.3 - Prob. 40ECh. 7.3 - How many different license plates are possible if...Ch. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Problems 45–48 refer to the following Venn...Ch. 7.3 - Problems 45–48 refer to the following Venn...Ch. 7.3 - A group of 75 people includes 32 who play tennis,...Ch. 7.3 - A class of 30 music students includes 13 who play...Ch. 7.3 - A group of 100 people touring Europe includes 42...Ch. 7.3 - A high school football team with 40 players...Ch. 7.3 - A management selection service classifies its...Ch. 7.3 - A corporation plans to fill 2 different positions...Ch. 7.3 - A sales representative who lives in city A wishes...Ch. 7.3 - A manufacturing company in city A wishes to truck...Ch. 7.3 - A survey of 1,200 people indicates that 850 own...Ch. 7.3 - A survey of 800 small businesses indicates that...Ch. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Prob. 66ECh. 7.4 - Find 6! Ch. 7.4 - Given the set {A, B, C, D}, how many permutations...Ch. 7.4 - Prob. 3MPCh. 7.4 - Prob. 4MPCh. 7.4 - Prob. 5MPCh. 7.4 - How many 5-card hands have 3 hearts and 2...Ch. 7.4 - Repeat Example 7 under the same conditions, except...Ch. 7.4 - Prob. 8MPCh. 7.4 - Prob. 9MPCh. 7.4 - Prob. 1EDCh. 7.4 - In Problems 1–6, evaluate the given expression...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - In Problems 1–6, evaluate the given expression...Ch. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - Prob. 14ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - Prob. 16ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - Prob. 21ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - Prob. 24ECh. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - In Problems 7–26, evaluate the expression. If the...Ch. 7.4 - In Problems 27–30, simplify each expression...Ch. 7.4 - In Problems 27–30, simplify each expression...Ch. 7.4 - In Problems 27–30, simplify each expression...Ch. 7.4 - In Problems 27–30, simplify each expression...Ch. 7.4 - In Problems 31–36, would you consider the...Ch. 7.4 - In Problems 31–36, would you consider the...Ch. 7.4 - In Problems 31–36, would you consider the...Ch. 7.4 - In Problems 31–36, would you consider the...Ch. 7.4 - In Problems 31–36, would you consider the...Ch. 7.4 - In Problems 31–36, would you consider the...Ch. 7.4 - In a horse race, how many different finishes among...Ch. 7.4 - In a long-distance foot race, how many different...Ch. 7.4 - How many ways can a 3-person subcommittee be...Ch. 7.4 - Nine cards are numbered with the digits from 1 to...Ch. 7.4 - From a standard 52-card deck, how many 6-card...Ch. 7.4 - From a standard 52-card deck, how many 6-card...Ch. 7.4 - From a standard 52-card deck, how many 5-card...Ch. 7.4 - From a standard 52-card deck, how many 5-card...Ch. 7.4 - From a standard 52-card deck, how many 7-card...Ch. 7.4 - From a standard 52-card deck, how many 7-card...Ch. 7.4 - From a standard 52-card deck, how many 4-card...Ch. 7.4 - From a standard 52-card deck, how many 4-card...Ch. 7.4 - From a standard 52-card deck, how many 5-card...Ch. 7.4 - From a standard 52-card deck, how many 5-card...Ch. 7.4 - A catering service offers K appetizers, 10 main...Ch. 7.4 - Three departments have 12, 15, and 18 members,...Ch. 7.4 - Prob. 53ECh. 7.4 - In Problems 53 and 54, refer to the table in the...Ch. 7.4 - In Problems 55–60, discuss the validity of each...Ch. 7.4 - In Problems 55–60, discuss the validity of each...Ch. 7.4 - In Problems 55–60, discuss the validity of each...Ch. 7.4 - In Problems 55–60, discuss the validity of each...Ch. 7.4 - In Problems 55–60, discuss the validity of each...Ch. 7.4 - In Problems 55–60, discuss the validity of each...Ch. 7.4 - Eight distinct points are selected on the...Ch. 7.4 - Five distinct points are selected on the...Ch. 7.4 - In how many ways can 4 people sit in a row of 6...Ch. 7.4 - In how many ways can 3 people sit in a row of 7...Ch. 7.4 - A basketball team has 5 distinct positions. Out of...Ch. 7.4 - How many 4-person committees are possible from a...Ch. 7.4 - Let U be the set of all 2-card hands, let K be the...Ch. 7.4 - Prob. 68ECh. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - An office supply store receives a shipment of 24...Ch. 7.4 - An electronics store receives a shipment of 30...Ch. 7.4 - A jewelry store chain with 8 stores in Georgia, 12...Ch. 7.4 - A real estate company with 14 employees in its...Ch. 7.4 - Suppose that 6 female and 5 male applicants have...Ch. 7.4 - A 4-person grievance committee is selected out of...Ch. 7.4 - A 4-person grievance committee is selected out of...Ch. 7.4 - Prob. 78ECh. 7.4 - A nominating convention will select a president...Ch. 7.4 - In how many different ways can 6 candidates for an...Ch. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - In Problems 11–14, describe each proposition as a...Ch. 7 - In Problems 15–16, state the converse and the...Ch. 7 - In Problems 15–16, state the converse and the...Ch. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Prob. 50RECh. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - Prob. 55RECh. 7 - Prob. 56RECh. 7 - Prob. 57RECh. 7 - Prob. 58RECh. 7 - Prob. 59RECh. 7 - Prob. 60RECh. 7 - Prob. 61RECh. 7 - Prob. 62RECh. 7 - Prob. 63RECh. 7 - Prob. 64RECh. 7 - Prob. 65RECh. 7 - Prob. 66RECh. 7 - Prob. 67RECh. 7 - Prob. 68RECh. 7 - Prob. 69RECh. 7 - Prob. 70RE
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