Problem 1CYU: There are five seats available in a sedan. In how many ways can five people be seated if only three... Problem 2CYU: 2. A multiple-choice exam contains 10 questions, each having 3 possible answers. Assuming you answer... Problem 1E: 1. Jolene wants to drive from her house to the grocery store and then to the library. If her GPS... Problem 2E: 2. There are three bridges from the west shore of a river to an island in the center, and three... Problem 3E: Travel Options If you can travel from Frederick, Maryland, to Baltimore, Maryland, by car, bus, or... Problem 4E: Travel Options Suppose that Maria wants to go from Florida to Maine via New York and can travel each... Problem 5E: Daytona 500 Forty-four race cars competed in the 2016 Daytona 500. Assuming no ties, how many... Problem 6E: Kentucky Derby Twenty horses competed in the 2016 Kentucky Derby. Assuming no ties, how many... Problem 7E: 7. Winners Twenty athletes enter an Olympic event. Assuming no ties, how many different... Problem 8E: 8. Ranking Teams A sportswriter is asked to rank six teams. How many different orderings are... Problem 9E: 9. Electing Captains A football squad can elect a captain and an assistant captain in 870 possible... Problem 10E: Club Officers A club can elect a president and a treasurer in 600 different ways. How many members... Problem 11E: 11. Group Picture A group of five boys and three girls is to be photographed.
(a) How many ways can... Problem 12E: Arranging Books Three history books and six novels are to be arranged on a bookshelf. (a) How many... Problem 13E: 13. Rearranging Letters How many different words (including nonsense words) can be formed by using... Problem 14E: Three-Letter Words How many different three-letter words (including nonsense words) are there in... Problem 15E: 15. Selecting an Outfit How many different outfits consisting of a coat and a hat can be selected... Problem 16E: Selecting an Outfit How many different outfits can be selected from two coats, four hats, and two... Problem 17E: Serial Numbers A computer manufacturer assigns serial numbers to its computers. The first symbol of... Problem 18E: 18. License Plates Suppose that a license plate consists of a nonzero digit followed by three... Problem 19E: Social Security Numbers How many Social Security numbers are available if the only restriction is... Problem 20E: 20. Call Letters In 1923, the Federal Communications Commission directed that all new radio stations... Problem 21E: 21. Area Codes Before 1995, three-digit area codes for the United States had the following... Problem 22E: 22. Area Codes Refer to Exercise 21. Beginning in 1995, restriction (ii) was lifted and any digit... Problem 23E: Palindromes A number or word is said to be a palindrome if it reads the same backward as forward... Problem 24E: Palindromes A number or word is said to be a palindrome if it reads the same backward as forward... Problem 25E: Palindromes A number or word is said to be a palindrome if it reads the same backward as forward... Problem 26E: 26. How many 3-letter words (including nonsense words) are palindromes?
Problem 27E: 27. World Series The World Series of Baseball is played between the American League and National... Problem 28E: 28. Super Bowl The Super Bowl is a game played between the National Football Conference and American... Problem 29E: 29. Bridge Games There are 3200 duplicate bridge clubs sanctioned by the American Contract Bridge... Problem 30E: Ice Cream Selections An ice cream parlor offers 25 flavors of ice cream. Assuming that order... Problem 31E: Internet Accounts A college of 20,000 students provides each student with an Internet account.... Problem 32E: 32. Pairs of Initials A company has 700 employees. Explain why there must be two people with the... Problem 33E: 33. Game Outcomes The final score in a soccer game is 6 to 4. How many different halftime scores are... Problem 34E: Selecting an Outfit Each day, Gloria dresses in a blouse, a skirt, and shoes. She wants to wear a... Problem 35E: Mismatched Gloves A man has five different pairs of gloves. In how many ways can he select a... Problem 36E: 36. Mismatched Shoes Fred has 11 different pairs of shoes. In how many ways can he put on a pair of... Problem 37E: Coin Tosses Toss a coin six times, and observe the sequence of heads and tails that results. How... Problem 38E: 38. Coin Tosses Refer to Exercise 37. In how many of the sequences are the first and last tosses... Problem 39E: 39. Exam Questions An exam contains five true-or-false questions. In how many different ways can the... Problem 40E: Exam Questions An exam contains five true-or-false questions. In how many ways can the exam be... Problem 41E: 41. Exam Questions Each of the 10 questions on a multiple choice exam has four possible answers. How... Problem 42E: 42. Exam Questions Rework Exercise 41 under the assumption that not every question must be... Problem 43E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 44E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 45E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 46E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 47E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 48E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 49E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 50E: ZIP Codes ZIP (Zone Improvement Plan) codes, sequences of five digits, were introduced by the United... Problem 51E: Shading of Venn Diagrams How many different ways can a Venn diagram with two circles be shaded? Problem 52E: Shading of Venn Diagrams How many different ways can a Venn diagram with three circles be shaded? Problem 53E: Roulette An American roulette wheel consists of 38 numbered pockets. Two of them (numbered 0 and 00)... Problem 54E: Roulette An American roulette wheel consists of 38 numbered pockets. Two of them (numbered 0 and 00)... Problem 55E: Batting Orders The manager of a Little League baseball team has picked the nine starting players for... Problem 56E: Test Volunteers A physiologist wants to test the effects of exercise and meditation on blood... Problem 57E: Handshakes Two 10-member basketball teams play a game. After the game, each of the members of the... Problem 58E: 58. Band Selections In how many ways can a band play a set of three waltzes and three tangos without... Problem 59E: 59. Colored Houses Six houses in a row are each to be painted with one of the colors red, blue,... Problem 60E: Chair Varieties A furniture manufacturer makes three types of upholstered chairs and offers 20... Problem 61E: 61. Ballots Seven candidates for mayor, four candidates for city council president, and six... Problem 62E: College Applications Allison is preparing her applications for college. She will apply to three... Problem 63E: Paths to Texas Consider the triangular display of letters below. Start with the letter T at the top... Problem 64E format_list_bulleted