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Math Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

The number of zeros that occur in the following factorial and then explain why this works. (a) Solution: The number of zeros in 13 ! = 2 ¯ Given: 13 ! Explanation: According to the definition of factorial: n ! = n × ( n − 1 ) × ( n − 2 ) ⋯ × 2 × 1 13 ! = 13 × 12 × 11 × 10 ⋯ × 2 × 1 So, number of 5’s in 13 ! is two times (factor 5 and 10), so 13 ! has two ending zeros in its calculation. Conclusion: The number of zeros in 13 ! = 2 ¯ . (b) Solution: The number of zeros in 27 ! = 6 ¯ Given: 27 ! Explanation: According to the definition of factorial: n ! = n × ( n − 1 ) × ( n − 2 ) ⋯ × 2 × 1 27 ! = 27 × 26 × 25 × 24 ⋯ × 2 × 1 So, the number of 27 ! is 6 (factor 5, 10, 15, and 20) and two factors in 25 , so 27 ! has 6 ending zeros in its calculation. Concept of zeros in any factorial comes from multiplying 5 into 2. Multiply by one 5 into one 2 calculate 10. So, one 5 and one 2 gives one zero at the end of calculation. So, the number of zeros in any factorial depends on the number of 5’s and the number of 2’s in its factor. Conclusion: The number of zeros in 27 ! = 6 ¯ (c) Solution: The number of zeros in 75 ! = 18 Given: 75 ! Explanation: According to the definition of factorial: n ! = n × ( n − 1 ) × ( n − 2 ) ⋯ × 2 × 1 75 ! = 75 × 74 × 73 × ⋯ × 2 × 1 . So, the number of 5’s in factorial 75 is 18 times: Factor 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 in this factor out of which the element 25, 50, and 75 consists of two 5’s. So, 75 ! has 18 ending zeros in its calculation. Concept of zeros in any factorial comes from multiplying 5 into 2. Multiply by one 5 into one 2 to calculate 10. So, one 5 and one 2 gives one zero at the end of the calculation. So, the number of zeros in any factorial depends on number of 5’s and number of 2’s in its factor. Conclusion: The number of zeros in 75 ! = 18

The number of zeros that occur in the following factorial and then explain why this works. (a) Solution: The number of zeros in 13 ! = 2 ¯ Given: 13 ! Explanation: According to the definition of factorial: n ! = n × ( n − 1 ) × ( n − 2 ) ⋯ × 2 × 1 13 ! = 13 × 12 × 11 × 10 ⋯ × 2 × 1 So, number of 5’s in 13 ! is two times (factor 5 and 10), so 13 ! has two ending zeros in its calculation. Conclusion: The number of zeros in 13 ! = 2 ¯ . (b) Solution: The number of zeros in 27 ! = 6 ¯ Given: 27 ! Explanation: According to the definition of factorial: n ! = n × ( n − 1 ) × ( n − 2 ) ⋯ × 2 × 1 27 ! = 27 × 26 × 25 × 24 ⋯ × 2 × 1 So, the number of 27 ! is 6 (factor 5, 10, 15, and 20) and two factors in 25 , so 27 ! has 6 ending zeros in its calculation. Concept of zeros in any factorial comes from multiplying 5 into 2. Multiply by one 5 into one 2 calculate 10. So, one 5 and one 2 gives one zero at the end of calculation. So, the number of zeros in any factorial depends on the number of 5’s and the number of 2’s in its factor. Conclusion: The number of zeros in 27 ! = 6 ¯ (c) Solution: The number of zeros in 75 ! = 18 Given: 75 ! Explanation: According to the definition of factorial: n ! = n × ( n − 1 ) × ( n − 2 ) ⋯ × 2 × 1 75 ! = 75 × 74 × 73 × ⋯ × 2 × 1 . So, the number of 5’s in factorial 75 is 18 times: Factor 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 in this factor out of which the element 25, 50, and 75 consists of two 5’s. So, 75 ! has 18 ending zeros in its calculation. Concept of zeros in any factorial comes from multiplying 5 into 2. Multiply by one 5 into one 2 to calculate 10. So, one 5 and one 2 gives one zero at the end of the calculation. So, the number of zeros in any factorial depends on number of 5’s and number of 2’s in its factor. Conclusion: The number of zeros in 75 ! = 18

Solution Summary: The author explains how the number of zeros in underset is determined by multiplying 5 into 2.

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.1, Problem 26E

Chapter 8.1, Problem 28E

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Chapter 8 Solutions

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - In Exercises 1-12, evaluate the factorial or...

Ch. 8.1 - Prob. 11E Ch. 8.1 - In Exercises 1 evaluate the factorial or...Ch. 8.1 - How many different types of homes are available if...Ch. 8.1 - A menu offers a choice of 3 salads, 8 main dishes,...Ch. 8.1 - Prob. 15E Ch. 8.1 - In a club with 16 members, how many ways can a...Ch. 8.1 - Define permutation in your own words.Ch. 8.1 - Explain the difference between distinguishable and...Ch. 8.1 - Prob. 19E Ch. 8.1 - In Example 6, how many unordered 2-letter subsets...Ch. 8.1 - Prob. 21E Ch. 8.1 - A printer has 5 A's, 4 B's, 2 C's, and 2 D's. How...Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Life Sciences Drug Sequencing Twelve drugs have...Ch. 8.1 - Prob. 35E Ch. 8.1 - Science Conference At an annual college science...Ch. 8.1 - Social Sciences Social Science Experiment In an...Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Union Elections A chapter of union Local 715 has...Ch. 8.1 - Prob. 41E Ch. 8.1 - Programming Music A zydeco band from Louisiana...Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - IP Addresses Every computer or other device...Ch. 8.1 - License Plates For many years, the state of...Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Traveling Salesman In the famous Traveling...Ch. 8.1 - Prob. 55E Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - In how many ways can a hand of 6 red cards he...Ch. 8.2 - Prob. 13E Ch. 8.2 - An economics club has 31 members. (a) If a...Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - In Exercises #x2013;24, decide whether each...Ch. 8.2 - In Exercises 1724, decide whether each exercise...Ch. 8.2 - In Exercises 1724, decide whether each exercise...Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Assembly Line Sampling Five items are to be...Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Social Sciences Legislative Committee A...Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Passwords A certain website requires users to log...Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55E Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.3 - A basket contains 7 red apples and 4 yellow...Ch. 8.3 - A basket contains 7 red apples and 4 yellow...Ch. 8.3 - A basket contains 7 red apples and 4 yellow...Ch. 8.3 - A basket contains 7 red apples and yellow apples....Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - Two cards are drawn at random from an ordinary...Ch. 8.3 - Find the probability that the 2-card hand...Ch. 8.3 - Find the probability that the 2-card hand...Ch. 8.3 - Find the probability that the 2-card hand...Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Twenty-six slips of paper are each marked with a...Ch. 8.3 - Prob. 22E Ch. 8.3 - Discuss the relative merits of using tree diagrams...Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - For Exercises 25-28, refer to Example 6 in this...Ch. 8.3 - Prob. 27E Ch. 8.3 - For Exercises 25- refer to Example 6 in this...Ch. 8.3 - After studying all night for a final exam, a...Ch. 8.3 - Prob. 30E Ch. 8.3 - If the letters l, i, t, t, l, and e are chosen at...Ch. 8.3 - If the letters M, i, s. s. i, s, s, i, p, p, and i...Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Social Sciences Election Ballots Five names are...Ch. 8.3 - Native American Council At the first meeting of a...Ch. 8.3 - Prob. 46E Ch. 8.3 - Education At a conference promoting excellence in...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - General Interest Poker Find the probabilities of...Ch. 8.3 - Prob. 55E Ch. 8.3 - Prob. 56E Ch. 8.3 - Prob. 57E Ch. 8.3 - Prob. 58E Ch. 8.3 - Prob. 59E Ch. 8.3 - Prob. 60E Ch. 8.3 - Prob. 61E Ch. 8.3 - Prob. 62E Ch. 8.3 - Prob. 63E Ch. 8.3 - Prob. 64E Ch. 8.3 - Prob. 65E Ch. 8.3 - Prob. 66E Ch. 8.3 - Prob. 67E Ch. 8.3 - Lottery An article in The New York Times...Ch. 8.3 - Prob. 69E Ch. 8.3 - Prob. 70E Ch. 8.3 - Prob. 71E Ch. 8.3 - Prob. 72E Ch. 8.3 - Football During the 1988 college football season,...Ch. 8.3 - Prob. 74E Ch. 8.3 - Bingo Bingo has become popular in the United...Ch. 8.3 - Prob. 76E Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - Suppose that a family has 5 children. Also,...Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - Suppose that a family has S children. Also,...Ch. 8.4 - A die is rolled 12 times. Find the probabilities...Ch. 8.4 - A die is rolled 12 times. Find the probabilities...Ch. 8.4 - A die is rolled 12 times. Find the probabilities...Ch. 8.4 - A die is rolled times. Find the probabilities of...Ch. 8.4 - A die is rolled 12 times. Find the probabilities...Ch. 8.4 - A die is rolled 12 times. Find the probabilities...Ch. 8.4 - How do you identify a probability problem that...Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Business and Economics Management The survey...Ch. 8.4 - Business and Economics Management The survey...Ch. 8.4 - Business and Economics Management The survey...Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Quality Control A factory tests a random sample of...Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Pecans Pecan producers blow air through the pecans...Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Life Sciences Breast Cancer A recent study found...Ch. 8.4 - Prob. 37E Ch. 8.4 - Life Sciences Breast Cancer A recent study found...Ch. 8.4 - Births of Twins The probability that a birth will...Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - Prob. 42E Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.4 - Prob. 48E Ch. 8.4 - Prob. 49E Ch. 8.4 - Volunteering A recent survey found that 83% of...Ch. 8.4 - Volunteering A recent survey found that 83% of...Ch. 8.4 - Volunteering A recent survey found that 83% of...Ch. 8.4 - Volunteering A recent survey found that 83% of...Ch. 8.4 - Minority Enrollment According to the U.S....Ch. 8.4 - Prob. 56E Ch. 8.4 - Prob. 57E Ch. 8.4 - Prob. 59E Ch. 8.5 - For each experiment described below, let x...Ch. 8.5 - For each experiment described below, let x...Ch. 8.5 - Prob. 3E Ch. 8.5 - For each experiment described below, let x...Ch. 8.5 - Prob. 5E Ch. 8.5 - Draw a histogram for the following, and shade the...Ch. 8.5 - Prob. 7E Ch. 8.5 - Draw a histogram for the following, and shade the...Ch. 8.5 - Prob. 9E Ch. 8.5 - Find the expected value for each random variable....Ch. 8.5 - Prob. 11E Ch. 8.5 - Find the expected value for each random variable....Ch. 8.5 - Prob. 13E Ch. 8.5 - Find the expected value for the random variable x...Ch. 8.5 - Prob. 15E Ch. 8.5 - Find the expected value for the random variable x...Ch. 8.5 - Prob. 17E Ch. 8.5 - Suppose one day Mary brings a 2-headed coin and...Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Business and Economics Complaints A local used-car...Ch. 8.5 - Payout on Insurance Policies An insurance company...Ch. 8.5 - Device Failure An insurance policy on an...Ch. 8.5 - Prob. 33E Ch. 8.5 - Rating Sales Accounts Levi Strauss and Company...Ch. 8.5 - Prob. 35E Ch. 8.5 - Life Sciences Animal Offspring In a certain animal...Ch. 8.5 - Ear Infections Otitis media, or middle ear...Ch. 8.5 - Hospitalization Insurance An insurance policy pays...Ch. 8.5 - Prob. 39E Ch. 8.5 - Prob. 40E Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Prob. 45E Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - The Hog Game In the hug game, each player states...Ch. 8.5 - Prob. 56E Ch. 8.5 - Prob. 57E Ch. 8 - Refer to the example and find the following. (a)...Ch. 8 - Which policy lends to the lowest expected cost?Ch. 8 - In the example, p1 + p2 + p3 = 0.09 + 0.24 + 0.17...Ch. 8 - Suppose an item to be repaired might need one of n...Ch. 8 - Prob. 1RE Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Determine whether each of the following statements...Ch. 8 - Prob. 5RE Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - Prob. 16RE Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Explain under what circumstances a permutation...Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - Prob. 32RE Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - In Exercises 41 and (a) give a probability...Ch. 8 - Prob. 43RE Ch. 8 - Prob. 44RE Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE Ch. 8 - Prob. 59RE Ch. 8 - Prob. 60RE Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 65RE Ch. 8 - Prob. 66RE Ch. 8 - Prob. 67RE Ch. 8 - Prob. 68RE Ch. 8 - Prob. 69RE Ch. 8 - Prob. 70RE Ch. 8 - Prob. 71RE Ch. 8 - Prob. 72RE Ch. 8 - Prob. 73RE Ch. 8 - Prob. 74RE Ch. 8 - Contests At one time, game boards for a United...Ch. 8 - Prob. 76RE Ch. 8 - Prob. 77RE Ch. 8 - Prob. 78RE Ch. 8 - Prob. 79RE Ch. 8 - Prob. 80RE Ch. 8 - Prob. 81RE Ch. 8 - Prob. 82RE

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