
Finite Mathematics For The Managerial, Life, And Social Sciences
12th Edition
ISBN: 9781337606592
Author: Tan
Publisher: CENGAGE L
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Textbook Question
Chapter 6.4, Problem 73E
CONTRACT BIDDING UBS Television Company is considering bids submitted by seven different firms for each of three different contracts. In how many ways can the contracts be awarded among these firms if no firm is to receive more than two contracts?
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2. In a computer network some pairs of computers are connected by network cables.
Your goal is to set up the computers so that messages can be sent quickly from any
computer to any other computer. For this you have identified each of the n com-
puters uniquely with a number between 1 and n, and have decided that a message
should consist of two such numbers, identifying the sender and the recipient, fol-
lowed by the content of the message. As cables are relatively short, you can assume
that sending a message across a single cable takes an amount of time that is the
same irrespective of the length of the cable. You can further assume that at most
one message travels between computer at any point, so that you don't have to worry
about inference among messages.
(a) Define a graph or network that models the computer network and allows you
to answer the remaining parts of this question.
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3. A spreadsheet consists of cells indexed by a row and a column. Each cell contains
either a value or a formula that depends on the values of other cells.
(a) Describe a graph, digraph, or network that models an arbitrary spreadsheet
and allows you to answer the remaining parts of this question.
(b) Explain, by referring to the graph, digraph, or network, when it is possible to
change the value of cell x without changing the value of cell y.
(c) Explain, by referring to the graph, digraph, or network, when it is possible to
calculate the values of all cells in the spreadsheet.
Consider the following spreadsheet with 5 rows, 7 columns, and 35 cells. For exam-
ple, cell el contains a value, whereas cell al contains a formula that depends on the
values cells el and 95.
a
b
с
1
el+g5 al-c5 110
d
al+cl 180
e
f
g
f5-el
c1+c2
2
al+b1 a2+c4 240
a2+c2 120
f5-e2
e3+e5
3 a2+b2 a3-c3 100
a3+c1 200
f5-e3 f1+f2
4
a3+b3 a4+c2 220
a4+c2 100 f5-e4 f3+f4
5 a4+b4 a5-c1 130 a5+c5 120 g3+g4 g1+g2
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1. Let W, U, and S be graphs defined as follows:
• V(W) is the set of countries in the world;
• V(U) is the set of countries in the European Union;
V(S) is the set of countries in the Schengen Area;
● for X = {W,U,S}, E(X) is the set of pairs of countries in V(X) that share a
land border.
Recall that land borders between countries in the Schengen Area are special in that
they can be crossed without a passport.
(a) The notions of a country and a land border are somewhat ambiguous. Explain
the notions you will use to get a precise definition of the graphs W, U, and S.
(b) Is S a subgraph of U? Is U an induced subgraph of W? Justify your answers.
(c) Using non-mathematical language, explain what it means for a country x if
VEV(S) and dw (v) = 0. Give all such countries.
Let A = {v Є V(W) \V(S) such that |Nw(v)| > 0 and Nw (v) ≤ V(S)}.
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Chapter 6 Solutions
Finite Mathematics For The Managerial, Life, And Social Sciences
Ch. 6.1 - Prob. 1CQCh. 6.1 - Prob. 2CQCh. 6.1 - Prob. 3CQCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7E
Ch. 6.1 - Prob. 8ECh. 6.1 - In Exercises 9-14, state whether the statements...Ch. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Let U denotes the set of all students who applied...Ch. 6.1 - In Exercise 27-28, write an expression describing...Ch. 6.1 - In Exercise 27-28, write an expression describing...Ch. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - In Exercise 35-38, let U={1,2,3,4,5,6,7,8,9,10},...Ch. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - BEST U.S. CITY FOR ITALIAN RESTAURANTS In a reader...Ch. 6.1 - INVENTORY Loss The biggest cause of inventory...Ch. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Prob. 72ECh. 6.1 - Prob. 73ECh. 6.1 - Prob. 74ECh. 6.1 - In Exercise 71-80, determine whether the statement...Ch. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Prob. 80ECh. 6.2 - Prob. 1CQCh. 6.2 - Prob. 2CQCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - If n(A)=15, n(AB)=5 and n(AB)=30, then what is...Ch. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - NEWSPAPER SUBSCRIBERS A survey of 1000 subscribers...Ch. 6.2 - JAIL INMATES On a certain day, the Wilton County...Ch. 6.2 - Of 100 clock radios with digital tuners and/or CD...Ch. 6.2 - COMPTER OWNERSHIP A survey of 100 college students...Ch. 6.2 - Prob. 22ECh. 6.2 - BRAND PREFERENCES OF CONSUMERS In a survey of 120...Ch. 6.2 - SPORTS CLUB SURVEY In a survey of 200 members of a...Ch. 6.2 - INVESTORS' USAGE OF BROKERS In a poll conducted...Ch. 6.2 - COMMUTER TRENDS Of 50 employees of a store located...Ch. 6.2 - CONSUMER SURVEY OF DESKTOP AND TABLET COMPUTER...Ch. 6.2 - CONSUMER SURVEY OF HDTV AND MP3 PLAYER OWNERS In a...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - In Exercises 3134, use the given information to...Ch. 6.2 - In Exercises 3134, use the given information to...Ch. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - BRAND SWITCHING AMONG FEMALE COLLEGE STUDENTSIn a...Ch. 6.2 - Prob. 41ECh. 6.2 - FEDERAL BUDGET ALLOCATION According to the Office...Ch. 6.2 - SURVEY OF LEADING ECONOMISTS A survey of the...Ch. 6.2 - STUDENT DROPOUT RATE Data released by the...Ch. 6.2 - STUDENT MAGAZINE PREFERENCES A survey of 100...Ch. 6.2 - SAT SCORES Results of a Department of Education...Ch. 6.2 - BRAND PREFERENCES OF CONSUMERS The 120 consumers...Ch. 6.2 - CAFETERIA STUDENT USAGE To help plan the number of...Ch. 6.2 - 401k INVESTMENTS In a survey of 200 employees of a...Ch. 6.2 - NEWSPAPER PREFERENCES OF INVESTORS In a survey of...Ch. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Prob. 56ECh. 6.3 - Explain the multiplication principle, and...Ch. 6.3 - Prob. 2CQCh. 6.3 - RENTAL RATES Lynbrook West, an apartment complex...Ch. 6.3 - COMMUTER PASSES Five different types of monthly...Ch. 6.3 - BLACKJACK In the game of blackjack, a 2-card hand...Ch. 6.3 - Prob. 4ECh. 6.3 - WARDROBE SELECTION A female executive selecting...Ch. 6.3 - COMMUTER OPTIONS Four commuter trains and three...Ch. 6.3 - PSYCHOLOGY EXPERIMENTS A psychologist has...Ch. 6.3 - Prob. 8ECh. 6.3 - HEALTH-CARE PLAN OPTIONS A new state employee is...Ch. 6.3 - CODE WORDS How many three-letter code words can be...Ch. 6.3 - Prob. 11ECh. 6.3 - MENU CHOICES The New Shanghai Restaurant offers a...Ch. 6.3 - CHOOSING A PIN Janice needs to make up a personal...Ch. 6.3 - MENU CHOICES Marias Trattoria offers mushrooms,...Ch. 6.3 - Prob. 15ECh. 6.3 - CHOOSING A DRIVER Five friends are leaving a bar...Ch. 6.3 - WRITTEN DRIVERs TEST The California drivers...Ch. 6.3 - BUILDING A PICKUP TRUCK The 2017 Sierra 1500...Ch. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - SERIAL NUMBERS Computers manufactured by a certain...Ch. 6.3 - COMPUTER DATING A computer dating service uses the...Ch. 6.3 - AUTOMOBILE COLOR AND TRIM CHOICES The 2017 BMW...Ch. 6.3 - AUTOMOBILE OPTIONS The 2017 Toyota Camry comes...Ch. 6.3 - TELEVISION-VIEWING POLLS An opinion poll is to be...Ch. 6.3 - LICENSE PLATE NUMBERS Over the years, the state of...Ch. 6.3 - POLITICAL POLLS An opinion poll was conducted by...Ch. 6.3 - LICENSE PLATE NUMBERS In recent years, the state...Ch. 6.3 - Exams An exam consists of ten true-or-false...Ch. 6.3 - WARRANTY NUMBERS A warranty identification number...Ch. 6.3 - CHOOSING A PASSWORD A password is to be made from...Ch. 6.3 - LOTTERIES In a state lottery, there are 15...Ch. 6.3 - COMBINATION LOCKS A rolling combination four-digit...Ch. 6.3 - COMBINATION LOCKS Lugano Leather Company makes an...Ch. 6.3 - TELEPHONE NUMBERS a. How many seven-digit...Ch. 6.3 - SLOT MACHINES A "lucky dollar" is one of the nine...Ch. 6.3 - STAFFING Student Painters, which specializes in...Ch. 6.3 - Prob. 39ECh. 6.3 - In Exercises 39 and 40, determine whether the...Ch. 6.4 - a. What is a permutation of a set of distinct...Ch. 6.4 - Prob. 2CQCh. 6.4 - a. How many combinations are there of a set of n...Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - In Exercises 1-22, evaluate the given expression....Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - In Exercise 1-22, evaluate the given expression....Ch. 6.4 - Prob. 22ECh. 6.4 - In Exercises 23-30, classify each problem...Ch. 6.4 - In Exercises 23-30, classify each problem...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - In Exercises 23-30, classify each problem...Ch. 6.4 - Prob. 31ECh. 6.4 - How many three-letter permutations can be formed...Ch. 6.4 - In how many ways can four students be seated in a...Ch. 6.4 - In how many ways can five people line up at a...Ch. 6.4 - Prob. 35ECh. 6.4 - In how many ways can the names of six candidates...Ch. 6.4 - In how many ways can a member of a hiring...Ch. 6.4 - In how many ways can an investor select four...Ch. 6.4 - Find the number of distinguishable permutations...Ch. 6.4 - Find the number of distinguishable permutations...Ch. 6.4 - In how many ways can the letters of the website...Ch. 6.4 - In how many ways can five people boarding a bus be...Ch. 6.4 - Prob. 43ECh. 6.4 - How many different signals can be made by hoisting...Ch. 6.4 - SUPERMARKET SITE SELECTION In how many ways can a...Ch. 6.4 - SELECTING A READING LIST A student is given a...Ch. 6.4 - QUALITY CONTROL In how many ways can a...Ch. 6.4 - STUDY GROUP ASSIGNMENTS A group of five students...Ch. 6.4 - TELEVISION PROGRAMMING In how many ways can a...Ch. 6.4 - WAITING LINES Seven people arrive at the ticket...Ch. 6.4 - SELECTING A SPECIAL OCCASION CAKE Fosselmans Ice...Ch. 6.4 - WEDDING CATERING L.A. Wedding Caterers offers a...Ch. 6.4 - MENU CHOICES Buca di Beppo, an Italian restaurant,...Ch. 6.4 - MANAGEMENT DECISIONS Weaver and Kline, a stock...Ch. 6.4 - CAR POOLS A company car that has a seating...Ch. 6.4 - Prob. 56ECh. 6.4 - TRAVEL WARDROBE Kaylee is planning a wardrobe for...Ch. 6.4 - Criminology The town of Carson employs 15 police...Ch. 6.4 - Book Exhibitions At a college library exhibition...Ch. 6.4 - CONCERT SEATING In how many ways can four married...Ch. 6.4 - Prob. 61ECh. 6.4 - Prob. 62ECh. 6.4 - NEWSPAPER ADS Four items from five different...Ch. 6.4 - MANAGEMENT DECISIONS C ** J Realty has received 12...Ch. 6.4 - SELECTING A BASEBALL TEAM A Little League baseball...Ch. 6.4 - TENNIS MATCH In the mens tennis tournament at...Ch. 6.4 - Prob. 67ECh. 6.4 - JURY SELECTION In how many different ways can a...Ch. 6.4 - Prob. 69ECh. 6.4 - EXAMS A student taking an examination is required...Ch. 6.4 - TEACHING ASSISTANTSHIPS Twelve graduate students...Ch. 6.4 - SENATE COMMITTIES In how many ways can a...Ch. 6.4 - CONTRACT BIDDING UBS Television Company is...Ch. 6.4 - PERSONNEL SELECTION JCL. Computers has five...Ch. 6.4 - Prob. 75ECh. 6.4 - WRITTEN DRIVERS TEST A state Motor Vehicle...Ch. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - Prob. 80ECh. 6.4 - Prob. 81ECh. 6.4 - Prob. 82ECh. 6.4 - Prob. 83ECh. 6.4 - WORLD SERIES In the World Series, one National...Ch. 6.4 - VOTING QUORUMS A quorum minimum of 6 voting...Ch. 6.4 - Prob. 86ECh. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.4 - Prob. 1TECh. 6.4 - Prob. 2TECh. 6.4 - Prob. 3TECh. 6.4 - Prob. 4TECh. 6.4 - Prob. 5TECh. 6.4 - Prob. 6TECh. 6.4 - In Exercises 110, evaluate the expression. C(52,7)Ch. 6.4 - Prob. 8TECh. 6.4 - In Exercises 110, evaluate the expression....Ch. 6.4 - In Exercises 110, evaluate the expression....Ch. 6.4 - Prob. 11TECh. 6.4 - Prob. 12TECh. 6.CRQ - Fill in the blanks. A well-defined collection of...Ch. 6.CRQ - Prob. 2CRQCh. 6.CRQ - Prob. 3CRQCh. 6.CRQ - Prob. 4CRQCh. 6.CRQ - Prob. 5CRQCh. 6.CRQ - Prob. 6CRQCh. 6.CRQ - Prob. 7CRQCh. 6.CRQ - Prob. 8CRQCh. 6.CRE - Prob. 1CRECh. 6.CRE - Prob. 2CRECh. 6.CRE - Prob. 3CRECh. 6.CRE - Prob. 4CRECh. 6.CRE - Prob. 5CRECh. 6.CRE - Prob. 6CRECh. 6.CRE - Prob. 7CRECh. 6.CRE - Prob. 8CRECh. 6.CRE - Prob. 9CRECh. 6.CRE - Prob. 10CRECh. 6.CRE - Prob. 11CRECh. 6.CRE - Prob. 12CRECh. 6.CRE - Prob. 13CRECh. 6.CRE - Prob. 14CRECh. 6.CRE - Prob. 15CRECh. 6.CRE - Prob. 16CRECh. 6.CRE - Prob. 17CRECh. 6.CRE - Prob. 18CRECh. 6.CRE - Prob. 19CRECh. 6.CRE - Prob. 20CRECh. 6.CRE - Prob. 21CRECh. 6.CRE - Prob. 22CRECh. 6.CRE - Prob. 23CRECh. 6.CRE - Prob. 24CRECh. 6.CRE - Prob. 25CRECh. 6.CRE - Let A and B be subsets of a universal set U and...Ch. 6.CRE - Prob. 27CRECh. 6.CRE - Prob. 28CRECh. 6.CRE - Prob. 29CRECh. 6.CRE - Prob. 30CRECh. 6.CRE - CREDIT CARD COMPARISONS A comparison of five major...Ch. 6.CRE - STUDENT SURVEYS The Department of Foreign...Ch. 6.CRE - In how many ways can six different DVDs be...Ch. 6.CRE - Prob. 34CRECh. 6.CRE - In how many ways can six different books, four of...Ch. 6.CRE - Prob. 36CRECh. 6.CRE - Find the number of distinguishable permutations...Ch. 6.CRE - Prob. 38CRECh. 6.CRE - AUTOMOBILE SELECTION An automobile manufacturer...Ch. 6.CRE - MENU SELECTIONS Two soups, five entres, and three...Ch. 6.CRE - Prob. 41CRECh. 6.CRE - POKER From a standard 52-card deck, how many...Ch. 6.CRE - Prob. 43CRECh. 6.CRE - TEAM SELECTION There are eight seniors and six...Ch. 6.CRE - Prob. 45CRECh. 6.CRE - SEATING ARRANGEMENTS In how many ways can seven...Ch. 6.CRE - Prob. 47CRECh. 6.CRE - Prob. 48CRECh. 6.CRE - Prob. 49CRECh. 6.CRE - Prob. 50CRECh. 6.BMO - Prob. 1BMOCh. 6.BMO - Prob. 2BMOCh. 6.BMO - In how many ways can four compact discs be...Ch. 6.BMO - Prob. 4BMOCh. 6.BMO - Prob. 5BMO
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