Finite Mathematics & Its Applications (12th Edition)
Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
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Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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Chapter 5.6, Problem 18E

Routes through City Streets Imagine a street map similar to the map in Fig. 3 but having r streets vertically and n − r street horizontally. Then, the number of shortest routes from A to B would be C ( n ,     r ) .

(a) Explain why the number of shortest routes A to D, the intersection directly north of B, would be C ( n − 1 ,     r − 1 ) .

(b) Explain why the number of shortest routes A to E, the intersection directly west of B, would be C ( n − 1 ,     r ) .

(c) Explain why C ( n − 1 ,     r − 1 ) + C ( n + 1 ,     r ) = C ( n ,     r ) .

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Chapter 5 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Solutions can be found following the section...Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7E
Ch. 5.1 - 8. Corporations Let {all corporations}, all...Ch. 5.1 - SP Index The Standard and Poors Index measures the...Ch. 5.1 - 10. S&P Index Refer to Table 3 on the next page....Ch. 5.1 - SP Index Refer to Exercise 9. Describe in words...Ch. 5.1 - 12. S&P Index Refer to Exercise 10. Describe in...Ch. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - In Exercises 15–20, simplify each given...Ch. 5.1 - In Exercises 1520, simplify each given expression....Ch. 5.1 - In Exercises 1520, simplify each given expression....Ch. 5.1 - Prob. 18ECh. 5.1 - In Exercises 15–20, simplify each given...Ch. 5.1 - Prob. 20ECh. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Corporation A large corporation classifies its...Ch. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - College Teachers and Students Let U= {people at...Ch. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - College Teachers and Students Let {people at Mount...Ch. 5.1 - College Teachers and Students Let {people at Mount...Ch. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - 47. Let U be the set of vertices in Fig. 1. Let, ...Ch. 5.1 - 48. Let U be the set of vertices in Fig. 1. Let, ...Ch. 5.1 - Sandwich Toppings Eds Cheesesteaks offers any...Ch. 5.1 - Toppings Choices Amy ordered a baked potato at a...Ch. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Find three subsets of the set of integers from 1...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 5562, determine whether the statement...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 5562, determine whether the statement...Ch. 5.1 - In Exercises 5562, determine whether the statement...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.1 - In Exercises 55–62, determine whether the...Ch. 5.2 - Prob. 1CYUCh. 5.2 - Prob. 2CYUCh. 5.2 - 1. Find , given that , and . Ch. 5.2 - Find n(ST), given that n(S)=17,n(T)=13, and...Ch. 5.2 - 3. Find , given that , and . Ch. 5.2 - Find n(ST), given that n(S)=4,n(T)=12, and...Ch. 5.2 - 5. Find , given that , and . Ch. 5.2 - 6. Find , given that , and . Ch. 5.2 - If n(S)=n(ST), what can you conclude about S and...Ch. 5.2 - If n(T)=n(ST), what can you conclude about S and...Ch. 5.2 - 9. Languages Suppose that each of the 314 million...Ch. 5.2 - 10. Course Enrollments Suppose that all of the...Ch. 5.2 - 11. Symmetry of Letters Of the 26 capital letters...Ch. 5.2 - 12. Streaming Subscriptions A survey of employees...Ch. 5.2 - Automobile Options Motors Inc. manufactured 325...Ch. 5.2 - 14. Investments A survey of 120 investors in...Ch. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - In Exercises 39–44, use De Morgan’s laws to...Ch. 5.2 - In Exercises 3944, use De Morgans laws to simplify...Ch. 5.2 - In Exercises 39–44, use De Morgan’s laws to...Ch. 5.2 - In Exercises 3944, use De Morgans laws to simplify...Ch. 5.2 - Prob. 43ECh. 5.2 - In Exercises 39–44, use De Morgan’s laws to...Ch. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - By drawing a Venn diagram, simplify each of the...Ch. 5.2 - Prob. 52ECh. 5.2 - By drawing a Venn diagram, simplify each of the...Ch. 5.2 - Prob. 54ECh. 5.2 - Citizenship Assume that the universal set U is the...Ch. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Citizenship Assume that the universal set U is the...Ch. 5.3 - Of the 1000 first-year students at a certain...Ch. 5.3 - 2. Refer to the Venn diagram from Problem...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Family Library The Venn diagram in Fig. 10...Ch. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Music Preferences A survey of 70 high school...Ch. 5.3 - 24. Nobel Winners A total of 900 Nobel Prizes had...Ch. 5.3 - 25. Analysis of Sonnet One of Shakespeare’s...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Exam Performance The results from an exam taken by...Ch. 5.3 - Class Enrollment Out of 35 students in a finite...Ch. 5.3 - Exercise Preferences A survey of 100 college...Ch. 5.3 - Exercises 33–38 refer to the 193 flags. 33. How...Ch. 5.3 - Exercises 3338 refer to the 193 flags. How many...Ch. 5.3 - Exercises 3338 refer to the 193 flags. How many...Ch. 5.3 - Exercises 33–38 refer to the 193 flags. 36. How...Ch. 5.3 - Exercises 33–38 refer to the 193 flags. 37. How...Ch. 5.3 - Exercises 3338 refer to the 193 flags. How many...Ch. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Course Enrollments Table 1 shows the number of...Ch. 5.3 - Prob. 46ECh. 5.3 - Use a Venn diagram to find the number of people in...Ch. 5.3 - Use a Venn diagram to find the number of people in...Ch. 5.3 - Prob. 49ECh. 5.3 - Use a Venn diagram to find the number of people in...Ch. 5.3 - 51. Voting Preferences One hundred college...Ch. 5.3 - Union Membership and Education Status A group of...Ch. 5.3 - Diagnostic Test Results A class of 30 students was...Ch. 5.3 - Air-Traffic Controllers A group of applicants for...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - College Majors A group of 61 students has the...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Music preferences A campus radio station surveyed...Ch. 5.3 - Website Preferences One hundred and sixty business...Ch. 5.3 - Small Businesses A survey of the characteristics...Ch. 5.3 - 71. Music Each of the 100 students attending a...Ch. 5.3 - Prob. 72ECh. 5.4 - There are five seats available in a sedan. In how...Ch. 5.4 - 2. A multiple-choice exam contains 10 questions,...Ch. 5.4 - 1. Jolene wants to drive from her house to the...Ch. 5.4 - 2. There are three bridges from the west shore of...Ch. 5.4 - Travel Options If you can travel from Frederick,...Ch. 5.4 - Travel Options Suppose that Maria wants to go from...Ch. 5.4 - Daytona 500 Forty-four race cars competed in the...Ch. 5.4 - Kentucky Derby Twenty horses competed in the 2016...Ch. 5.4 - 7. Winners Twenty athletes enter an Olympic event....Ch. 5.4 - 8. Ranking Teams A sportswriter is asked to rank...Ch. 5.4 - 9. Electing Captains A football squad can elect a...Ch. 5.4 - Club Officers A club can elect a president and a...Ch. 5.4 - 11. Group Picture A group of five boys and three...Ch. 5.4 - Arranging Books Three history books and six novels...Ch. 5.4 - 13. Rearranging Letters How many different words...Ch. 5.4 - Three-Letter Words How many different three-letter...Ch. 5.4 - 15. Selecting an Outfit How many different outfits...Ch. 5.4 - Selecting an Outfit How many different outfits can...Ch. 5.4 - Serial Numbers A computer manufacturer assigns...Ch. 5.4 - 18. License Plates Suppose that a license plate...Ch. 5.4 - Social Security Numbers How many Social Security...Ch. 5.4 - 20. Call Letters In 1923, the Federal...Ch. 5.4 - 21. Area Codes Before 1995, three-digit area codes...Ch. 5.4 - 22. Area Codes Refer to Exercise 21. Beginning in...Ch. 5.4 - Palindromes A number or word is said to be a...Ch. 5.4 - Palindromes A number or word is said to be a...Ch. 5.4 - Palindromes A number or word is said to be a...Ch. 5.4 - 26. How many 3-letter words (including nonsense...Ch. 5.4 - 27. World Series The World Series of Baseball is...Ch. 5.4 - 28. Super Bowl The Super Bowl is a game played...Ch. 5.4 - 29. Bridge Games There are 3200 duplicate bridge...Ch. 5.4 - Ice Cream Selections An ice cream parlor offers 25...Ch. 5.4 - Internet Accounts A college of 20,000 students...Ch. 5.4 - 32. Pairs of Initials A company has 700 employees....Ch. 5.4 - 33. Game Outcomes The final score in a soccer game...Ch. 5.4 - Selecting an Outfit Each day, Gloria dresses in a...Ch. 5.4 - Mismatched Gloves A man has five different pairs...Ch. 5.4 - 36. Mismatched Shoes Fred has 11 different pairs...Ch. 5.4 - Coin Tosses Toss a coin six times, and observe the...Ch. 5.4 - 38. Coin Tosses Refer to Exercise 37. In how many...Ch. 5.4 - 39. Exam Questions An exam contains five...Ch. 5.4 - Exam Questions An exam contains five true-or-false...Ch. 5.4 - 41. Exam Questions Each of the 10 questions on a...Ch. 5.4 - 42. Exam Questions Rework Exercise 41 under the...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - ZIP Codes ZIP (Zone Improvement Plan) codes,...Ch. 5.4 - Shading of Venn Diagrams How many different ways...Ch. 5.4 - Shading of Venn Diagrams How many different ways...Ch. 5.4 - Roulette An American roulette wheel consists of 38...Ch. 5.4 - Roulette An American roulette wheel consists of 38...Ch. 5.4 - Batting Orders The manager of a Little League...Ch. 5.4 - Test Volunteers A physiologist wants to test the...Ch. 5.4 - Handshakes Two 10-member basketball teams play a...Ch. 5.4 - 58. Band Selections In how many ways can a band...Ch. 5.4 - 59. Colored Houses Six houses in a row are each to...Ch. 5.4 - Chair Varieties A furniture manufacturer makes...Ch. 5.4 - 61. Ballots Seven candidates for mayor, four...Ch. 5.4 - College Applications Allison is preparing her...Ch. 5.4 - Paths to Texas Consider the triangular display of...Ch. 5.4 - Prob. 64ECh. 5.5 - Calculate the following values: (a) 5! (b) P(5,5)...Ch. 5.5 - 2. A newborn child is to be given a first name and...Ch. 5.5 - For Exercises 1–20, calculate the values. 1. Ch. 5.5 - For Exercises 120, calculate the values. P(5,1)Ch. 5.5 - For Exercises 1–20, calculate the values. 3. Ch. 5.5 - For Exercises 120, calculate the values. P(5,4)Ch. 5.5 - For Exercises 120, calculate the values. C(10,3)Ch. 5.5 - For Exercises 1–20, calculate the values. 6. Ch. 5.5 - For Exercises 120, calculate the values. C(5,4)Ch. 5.5 - For Exercises 120, calculate the values. C(6,3)Ch. 5.5 - For Exercises 120, calculate the values. P(7,1)Ch. 5.5 - For Exercises 1–20, calculate the values. 10. Ch. 5.5 - For Exercises 120, calculate the values. P(n,1)Ch. 5.5 - For Exercises 120, calculate the values. P(n,2)Ch. 5.5 - For Exercises 120, calculate the values. C(4,4)Ch. 5.5 - For Exercises 120, calculate the values. C(n,2)Ch. 5.5 - For Exercises 1–20, calculate the values. 15. Ch. 5.5 - For Exercises 120, calculate the values. C(n,1)Ch. 5.5 - For Exercises 1–20, calculate the values. 17. Ch. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - For Exercises 120, calculate the values. 7!Ch. 5.5 - In Exercises 2126, determine whether the...Ch. 5.5 - In Exercises 2126, determine whether the...Ch. 5.5 - In Exercises 21–26, determine whether the...Ch. 5.5 - In Exercises 21–26, determine whether the...Ch. 5.5 - In Exercises 21–26, determine whether the...Ch. 5.5 - In Exercises 2126, determine whether the...Ch. 5.5 - 27. Group Picture In how many ways can four people...Ch. 5.5 - 28. Waiting in Line In how many ways can six...Ch. 5.5 - Book Selection How many different selections of...Ch. 5.5 - Pizza Varieties A pizzeria offers five toppings...Ch. 5.5 - Selecting Colleges A high school student decides...Ch. 5.5 - Senate Committees In how many different ways can a...Ch. 5.5 - 33. Ranking Teams A sportswriter makes a preseason...Ch. 5.5 - 34. CD Changer Suppose that you have 36 CDs and...Ch. 5.5 - Guest Lists How many ways can you choose five out...Ch. 5.5 - Choosing Exam Questions A student is required to...Ch. 5.5 - 37. DVDs In a batch of 100 DVDs, seven are...Ch. 5.5 - Debates There are 17 candidates for an elected...Ch. 5.5 - 39. Race Winners Theoretically, assuming no ties,...Ch. 5.5 - 40. Player Introductions The five starting players...Ch. 5.5 - Poker Hands Exercises 41–44 refer to poker hands....Ch. 5.5 - Poker Hands Exercises 4144 refer to poker hands. A...Ch. 5.5 - Poker Hands Exercises 41–44 refer to poker hands....Ch. 5.5 - Poker Hands Exercises 4144 refer to poker hands. A...Ch. 5.5 - 45. Distributing Sandwiches Five students order...Ch. 5.5 - 46. Nautical Signals A nautical signal consists of...Ch. 5.5 - 47. Selecting Sweaters Suppose that you own 10...Ch. 5.5 - Distributing Books Fred has 12 different books....Ch. 5.5 - Conference Games In an eight-team football...Ch. 5.5 - 50. League Games In a six-team softball league,...Ch. 5.5 - Powerball In the Powerball lottery, five white...Ch. 5.5 - Baseball Lineup On a childrens baseball team,...Ch. 5.5 - Lotto Exercises 53 and 54 refer to the New York...Ch. 5.5 - Lotto Exercises 53 and 54 refer to the New York...Ch. 5.5 - Choosing Candy Two children, Moe and Joe, are...Ch. 5.5 - Committee Selection The 12 members of the Gotham...Ch. 5.5 - Group Picture The student council at Gotham...Ch. 5.5 - Arranging Books George has three books by each of...Ch. 5.5 - Seating Arrangements In the quiz show Its...Ch. 5.5 - Displaying Paintings An art gallery has four...Ch. 5.5 - 61. Handshakes At a party, everyone shakes hands...Ch. 5.5 - 62. Football Games In a football league, each team...Ch. 5.5 - 63. Side Dishes A restaurant offers its customers...Ch. 5.5 - Ice Cream Specials An ice cream parlor offers a...Ch. 5.5 - 65. Determine Position There are six-letter words...Ch. 5.5 - Detour-Prone ZIP Codes A five-digit ZIP code is...Ch. 5.5 - 67. Lottery (a) Calculate the number of possible...Ch. 5.5 - Bridge A bridge hand contains 13 cards. (a) What...Ch. 5.5 - 69. Cards versus Atoms Are there more ways to...Ch. 5.5 - Alphabet versus Atoms Are there more ways to...Ch. 5.6 - School Board A newspaper reporter wants an...Ch. 5.6 - 2. Free Throws A basketball player shoots eight...Ch. 5.6 - 1. Tossing a Coin An experiment consists of...Ch. 5.6 - 2. Tossing a Coin An experiment consists of...Ch. 5.6 - 3. Tossing a Coin An experiment consists of...Ch. 5.6 - 4. Tossing a Coin An experiment consists of...Ch. 5.6 - 5. World Series In the World Series, the American...Ch. 5.6 - World Series Refer to Exercise 5. How many...Ch. 5.6 - Game Outcomes A football team plays 11 games. In...Ch. 5.6 - 8. Game Outcomes A chess master plays 15 games. In...Ch. 5.6 - Bytes Exercises 9 and 10 refer to computer bytes....Ch. 5.6 - Bytes Exercises 9 and 10 refer to computer bytes....Ch. 5.6 - 11. Routes through City Streets Refer to the map...Ch. 5.6 - Routes through City Streets Refer to the map in...Ch. 5.6 - Routes through City Streets Refer to the map in...Ch. 5.6 - Routes through City Streets Refer to the map in...Ch. 5.6 - 15. Routes through City Streets Refer to the map...Ch. 5.6 - 16. Routes through City Streets Refer to the map...Ch. 5.6 - 17. Routes through City Streets Refer to the map...Ch. 5.6 - Routes through City Streets Imagine a street map...Ch. 5.6 - Tossing a Coin A coin is tossed 10 times, and the...Ch. 5.6 - 20. Arranging Books Four mathematics books and...Ch. 5.6 - 21. Seating Arrangements In how many ways can six...Ch. 5.6 - Photo Session In 2015, there were three women and...Ch. 5.6 - 23. Selecting Balls from an Urn An urn contains 12...Ch. 5.6 - 24. Selecting Balls from an Urn An urn contains 15...Ch. 5.6 - Selecting Apples A bag of 10 apples contains 2...Ch. 5.6 - Selecting Light Bulbs A package contains 100 LED...Ch. 5.6 - Subcommittee Selection A committee has four male...Ch. 5.6 - 28. Investment Portfolio In how many ways can an...Ch. 5.6 - Poker Hands Exercises 29–32 refer to poker hands....Ch. 5.6 - Poker Hands Exercises 2932 refer to poker hands. A...Ch. 5.6 - Poker Hands Exercises 2932 refer to poker hands. A...Ch. 5.6 - Poker Hands Exercises 2932 refer to poker hands. A...Ch. 5.6 - In Exercises 33–36, a “word” is interpreted to be...Ch. 5.6 - In Exercises 33–36, a “word” is interpreted to be...Ch. 5.6 - In Exercises 3336, a word is interpreted to be a...Ch. 5.6 - In Exercises 33–36, a “word” is interpreted to be...Ch. 5.6 - Photo Session In 2015, there were three women and...Ch. 5.6 - 38. Seating Arrangements You, a friend, and four...Ch. 5.6 - Numbers In how many five-digit numbers (without...Ch. 5.6 - Alphabetical Order In how many four-letter words...Ch. 5.6 - License Plates Suppose that license plates from a...Ch. 5.6 - 42. License Plates Suppose that license plates...Ch. 5.6 - Seating Arrangements A family has 12 members. In...Ch. 5.6 - Prob. 44ECh. 5.6 - Prob. 45ECh. 5.6 - Tossing a Coin What percent of the possible...Ch. 5.6 - Prob. 47ECh. 5.6 - 48. Selecting Balls from an Urn Suppose that a...Ch. 5.7 - Calculate (128).Ch. 5.7 - 2. An ice cream parlor offers 10 flavors of ice...Ch. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Calculate the value for each of Exercises...Ch. 5.7 - Calculate the value for each of Exercises...Ch. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Prob. 9ECh. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Prob. 13ECh. 5.7 - Prob. 14ECh. 5.7 - Prob. 15ECh. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Calculate the value for each of Exercises...Ch. 5.7 - Calculate the value for each of Exercises 1-18....Ch. 5.7 - Prob. 19ECh. 5.7 - How many terms are there in the binomial expansion...Ch. 5.7 - 21. Determine the first three terms in the...Ch. 5.7 - 22. Determine the first three terms in the...Ch. 5.7 - 23. Determine the last three terms in the binomial...Ch. 5.7 - Determine the last three terms in the binomial...Ch. 5.7 - Determine the middle term in the binomial...Ch. 5.7 - 26. Determine the middle term in the binomial...Ch. 5.7 - Determine the coefficient of x2 in the expansion...Ch. 5.7 - 28. Determine the coefficient in the expansion of...Ch. 5.7 - 29. Determine the coefficient of in binomial...Ch. 5.7 - 30. Determine the coefficient of in the binomial...Ch. 5.7 - Determine the first three terms in the binomial...Ch. 5.7 - 32. Determine the last three terms in the binomial...Ch. 5.7 - 33. Determine the middle term in the binomial...Ch. 5.7 - Determine the coefficient of x4y2 in the binomial...Ch. 5.7 - Prob. 35ECh. 5.7 - 36. Determine the term containing in the...Ch. 5.7 - Prob. 37ECh. 5.7 - 38. How many different subsets can be chosen from...Ch. 5.7 - Restaurant Tip How many different tips could you...Ch. 5.7 - 40. Pizza Options A pizza parlor offers mushrooms,...Ch. 5.7 - Cable TV Options A cable TV franchise offers 20...Ch. 5.7 - 42. Salad Options A salad bar offers a base of...Ch. 5.7 - Tie Selection In how many ways can a selection of...Ch. 5.7 - Dessert Choices In how many ways can a selection...Ch. 5.7 - Prob. 45ECh. 5.7 - Ice Cream Sundaes An ice cream parlor offers four...Ch. 5.7 - 47. Appetizer Selection In how many ways can a...Ch. 5.7 - CD Selection In how many ways can a selection of...Ch. 5.7 - Lab Projects Students in a physics class are...Ch. 5.7 - 50. Election A voter is asked to vote for at most...Ch. 5.7 - CD Selection James has nine jazz CDs and ten top...Ch. 5.7 - Book Selection Sarah has five nonfiction and six...Ch. 5.7 - 53. Can be a term of a binomial expansion? Ch. 5.7 - Can (85)x3 be a term of a binomial expansion?Ch. 5.7 - Prob. 55ECh. 5.7 - (a) Use equation (3) to show that...Ch. 5.7 - Find a simple expression for the value of...Ch. 5.7 - 58. Seating Passengers A blue van and a red van,...Ch. 5.8 - 1. A foundation wishes to award one grant of...Ch. 5.8 - 2. In how many different ways can six medical...Ch. 5.8 - Prob. 1ECh. 5.8 - Prob. 2ECh. 5.8 - Prob. 3ECh. 5.8 - Prob. 4ECh. 5.8 - Let S be a set of n elements. Determine the number...Ch. 5.8 - Let S be a set of n elements. Determine the number...Ch. 5.8 - Prob. 7ECh. 5.8 - Prob. 8ECh. 5.8 - Prob. 9ECh. 5.8 - Prob. 10ECh. 5.8 - Prob. 11ECh. 5.8 - Let S be a set of n elements. Determine the number...Ch. 5.8 - Prob. 13ECh. 5.8 - Prob. 14ECh. 5.8 - 15. Stock Reports A brokerage house regularly...Ch. 5.8 - 16. Investment Ratings An investment advisory...Ch. 5.8 - 17. RIFFRAFF How many eight-letter words consist...Ch. 5.8 - RAZZMATAZZ How many 10-letter words consist of one...Ch. 5.8 - 19. Postage Stamps In how many ways can three...Ch. 5.8 - 20. Nautical Signals A nautical signal consists of...Ch. 5.8 - 21. Observation Groups A psychology experiment...Ch. 5.8 - 22. Orientation Groups During orientation, new...Ch. 5.8 - 23. Weather In a certain month (of 30 days) it...Ch. 5.8 - Awarding Prizes Of the nine contestants in a...Ch. 5.8 - Job Promotions A corporation has four employees...Ch. 5.8 - 26. Forming Committees The 10 members of a city...Ch. 5.8 - 27. Field Trip In how many ways can the 14...Ch. 5.8 - 28. Work Schedule A sales representative must...Ch. 5.8 - 29. Basketball Teams Ten students in a physical...Ch. 5.8 - Sorting Sweaters In how many ways can 12 sweaters...Ch. 5.8 - Prob. 31ECh. 5.8 - Prob. 32ECh. 5.8 - Prob. 33ECh. 5.8 - 34. Campaign Tasks Calculate the number of ways...Ch. 5.8 - Prob. 35ECh. 5 - Prob. 1FCCECh. 5 - Prob. 2FCCECh. 5 - Prob. 3FCCECh. 5 - Define a universal set.Ch. 5 - 5. Define the empty set. Ch. 5 - Prob. 6FCCECh. 5 - Prob. 7FCCECh. 5 - Prob. 8FCCECh. 5 - Prob. 9FCCECh. 5 - Prob. 10FCCECh. 5 - Prob. 11FCCECh. 5 - Prob. 12FCCECh. 5 - Prob. 13FCCECh. 5 - Prob. 14FCCECh. 5 - Prob. 15FCCECh. 5 - Prob. 16FCCECh. 5 - 17. Explain what is meant by an ordered partition...Ch. 5 - Prob. 18FCCECh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - 4. Team Picture In how many ways can a coach and...Ch. 5 - Prob. 5RECh. 5 - Determine the first three terms in the binomial...Ch. 5 - Balls in an Urn An urn contains 14 numbered balls,...Ch. 5 - 8. Testing a Drug Sixty people with a certain...Ch. 5 - 9. Appliance Purchase An appliance store carries...Ch. 5 - 10. Contest Prizes There are 12 contestants in a...Ch. 5 - 11. Languages Out of a group of 115 applicants for...Ch. 5 - Calculate (1715).Ch. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - Prob. 19RECh. 5 - Environmental Poll The 100 members of the Earth...Ch. 5 - 21. Nine-Letter Words How many different...Ch. 5 - Prob. 22RECh. 5 - Winter Sports A survey at a small New England...Ch. 5 - 24. Meal Choices How many different meals can be...Ch. 5 - 25. Test Scoring On an essay test, there are five...Ch. 5 - 26. Seven-Digit Numbers How many seven-digit...Ch. 5 - Telephone Numbers How many telephone numbers are...Ch. 5 - Three-Digit Numbers How many three-digit numbers...Ch. 5 - Eight-Letter Words How many strings of length 8...Ch. 5 - Basketball Teams How many different five-person...Ch. 5 - 31. Selecting Students Fourteen students in the...Ch. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Filling Jobs Sixty people apply for 10 job...Ch. 5 - Generating Tests A computerized test generator can...Ch. 5 - 36. Six-Letter Words If a string of six letters...Ch. 5 - 37. Choosing Delegations How many different...Ch. 5 - Prob. 38RECh. 5 - Distributing Candy In how many ways can 14...Ch. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - 42. Softball League If every team in a 10-team...Ch. 5 - Diagonals How many diagonals does an n-sided...Ch. 5 - 44. Racetrack Betting Racetracks have a compound...Ch. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Poker How many hands of five cards contain exactly...Ch. 5 - Three-Digit Numbers How many three-digit numbers...Ch. 5 - 50. Three-Digit Numbers How many three-digit...Ch. 5 - Baseball In Exercises 51 and 52, suppose there are...Ch. 5 - Baseball In Exercises 51 and 52, suppose there are...Ch. 5 - Greek-Letter Societies Fraternity and sorority...Ch. 5 - 54. Family Picture A family consisting of two...Ch. 5 - Prob. 55RECh. 5 - 56. Splitting Classes Two elementary school...Ch. 5 - Prob. 57RECh. 5 - Arranging Books A set of books can be arranged on...Ch. 5 - Batting Order How many batting orders are possible...Ch. 5 - 60. Choosing Committees In the United States...Ch. 5 - Voting Suppose that you are voting in an election...Ch. 5 - Spelling Algebra The object is to start with the...Ch. 5 - Prob. 63RECh. 5 - Prob. 64RECh. 5 - Prob. 65RECh. 5 - Prob. 66RECh. 5 - Prob. 67RECh. 5 - Prob. 68RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Prob. 73RECh. 5 - Prob. 74RECh. 5 - 75. Express in your own words the difference...Ch. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 - Prob. 78RECh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - In the following triangular table, known as...Ch. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9P

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