(a) Explanation The numbers between 100 and 999 has three digits. Let the digit on the left be the first digit. There are 10 choices- 0 , 1 , … , 9 in total First find the numbers with no 5’s. For such numbers, there are 8 choices for the first digit since 0 and 5 cannot be considered and 9 choices each for the second and third digits since 0 cannot be considered. So, there are 8 × 9 × 9 = 648 choices in total. Now find the numbers with two 5’s. In such numbers, there will be 2 fives and one non-5 digit. If the non-5 digit goes in the first place, it can have one of the eight values (the eight digits except 0 and 5). If it goes in the second or third place, it can have one of the 9 values (the nine digits except 5) (b) To determine The answer to part (a) directly by creating a tree diagram and considering whether the first digit is a 5 or not, then the second digit, and then the third.

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

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

Publisher: PEARSON

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Question

Chapter 8.2, Problem 26E

(a)

To determine

The numbers between 100 and 999 which contain exactly one 5 by subtracting the number that contain no 5’s, or three 5’s from the total.

(b)

To determine

The answer to part (a) directly by creating a tree diagram and considering whether the first digit is a 5 or not, then the second digit, and then the third.

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Chapter 8.2, Problem 25E

Chapter 8.2, Problem 27E

Chapter 8 Solutions

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

Ch. 8.1 - A combination lock can be set to open to any...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 5YT Ch. 8.1 - Prob. 6YT Ch. 8.1 - Prob. 7YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E

Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Find the number of distinguishable permutations of...Ch. 8.1 - Prob. 22E 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 - InvestmentsKristen Elmores financial advisor has...Ch. 8.1 - SchedulingA local television station has eleven...Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Union ElectionsA chapter of union Local 715 has 35...Ch. 8.1 - Programming MusicA concert to raise money for an...Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Telephone Area CodesSeveral years ago, the United...Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E 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 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.2 - Prob. 1YT Ch. 8.2 - Prob. 2YT Ch. 8.2 - Solve the problems in Example 4. EXAMPLE...Ch. 8.2 - Prob. 4YT Ch. 8.2 - Prob. 5YT Ch. 8.2 - Prob. 1WE Ch. 8.2 - Prob. 2WE 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 - Prob. 12E Ch. 8.2 - Five cards are marked with the numbers I. 2. 3.4....Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - Prob. 18E Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - Prob. 20E Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - Prob. 22E Ch. 8.2 - In Exercises 17-24, decide whether each exercise...Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - The following problem was posed on National Public...Ch. 8.2 - Prob. 28E Ch. 8.2 - Work AssignmentsFrom a group of 8 newly hired...Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Worker GrievancesA group of 9 workers decides to...Ch. 8.2 - Prob. 33E Ch. 8.2 - Ice Cream FlavorsBaskin-Robbins advertises that it...Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Legislative CommitteeA legislative committee...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 - BaseballIf a baseball coach has 5 good hitters and...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 - License PlatesOfficials from a particular state...Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - AppetizersApplebees restaurant recently advertised...Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.3 - Prob. 1YT Ch. 8.3 - Prob. 2YT Ch. 8.3 - Suppose the container in Example 3 has 4...Ch. 8.3 - In Example 4, what is the probability of a hand...Ch. 8.3 - Prob. 5YT Ch. 8.3 - Prob. 6YT Ch. 8.3 - Prob. 1WE Ch. 8.3 - If the Senate has 59 Democrats and 41 Republicans,...Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - A basket contains 7 red apples and 4 yellow...Ch. 8.3 - In a club with 9 male and 11 female members, a...Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Find the probability that the 2-card hand...Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Twenty-six slips of paper are each marked with a...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 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - An elevator has 4 passengers and slops at 7...Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Quality ControlA shipment of 11 printers contains...Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Refer to Example 3. The managers feel that the...Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Prob. 44E Ch. 8.3 - Prob. 45E Ch. 8.3 - Prob. 46E Ch. 8.3 - EducationEducation At a conference promoting...Ch. 8.3 - PokerFind the probabilities of the following hands...Ch. 8.3 - Prob. 49E Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.3 - Prob. 52E Ch. 8.3 - Prob. 53E Ch. 8.3 - Prob. 54E 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 - Prob. 68E Ch. 8.3 - Prob. 69E Ch. 8.3 - Prob. 70E Ch. 8.3 - Prob. 71E Ch. 8.3 - Prob. 72E Ch. 8.3 - FootballDuring the 1988 college football season,...Ch. 8.3 - Prob. 74E Ch. 8.3 - Prob. 75E Ch. 8.3 - Prob. 76E Ch. 8.4 - Prob. 1YT Ch. 8.4 - Prob. 2YT Ch. 8.4 - Prob. 3YT Ch. 8.4 - Prob. 1WE Ch. 8.4 - Prob. 2WE Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - A die is rolled 12 times. Find the probabilities...Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E 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 - Prob. 22E Ch. 8.4 - Business and Economics ManagementThe survey...Ch. 8.4 - Prob. 24E Ch. 8.4 - Credit CardsA survey of consumer finance found...Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - BirthsIn Clay County, North Carolina, 54 out of 84...Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 45E Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.4 - Prob. 48E Ch. 8.4 - Health StudyA study is being conducted in which...Ch. 8.4 - Social Sciences 50. Women WorkingA recent study...Ch. 8.4 - Prob. 51E Ch. 8.4 - Prob. 52E Ch. 8.4 - Prob. 53E Ch. 8.4 - Prob. 54E Ch. 8.4 - Prob. 55E Ch. 8.4 - Prob. 56E Ch. 8.4 - Prob. 57E Ch. 8.4 - Prob. 58E Ch. 8.4 - SportsIn many spans championships, such as the...Ch. 8.5 - Prob. 1YT Ch. 8.5 - Prob. 2YT Ch. 8.5 - Prob. 3YT Ch. 8.5 - Prob. 4YT Ch. 8.5 - Prob. 5YT Ch. 8.5 - Prob. 1WE Ch. 8.5 - Prob. 2WE Ch. 8.5 - Prob. 1E 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 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - Prob. 12E Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - For the game in Example 5, find Marys expected...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 - Solve each exercise. Many of these exercises...Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Suppose someone offers to pay you 5 if you draw 2...Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Prob. 30E Ch. 8.5 - Payout on Insurance PoliciesAn insurance company...Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.5 - Hospitalization InsuranceAn insurance policy pays...Ch. 8.5 - Prob. 39E Ch. 8.5 - Prob. 40E Ch. 8.5 - Samuel AlitoWhen Supreme Court Justice Samuel...Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Prob. 45E Ch. 8.5 - RaffleA raffle offers a first prize of 1000, 2...Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Find the expected payback for the games of chance...Ch. 8.5 - Prob. 52E Ch. 8.5 - ContestsA magazine distributor offers a first...Ch. 8.5 - ContestsA contest at a fast-food restaurant...Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.5 - Prob. 57E Ch. 8 - Prob. 1RE Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE 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 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - A basket contains 4 black, 2 blue, and 7 green...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 - Suppose 2 cards are drawn without replacement from...Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - In Exercises 41 and 42, (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 - Suppose someone offers to pay you 100 if you draw...Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Job QualificationsOf the 12 people applying for an...Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE Ch. 8 - Identity TheftAccording to a survey by Javelin...Ch. 8 - Prob. 60RE Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Injury ClaimsThe number of injury claims per month...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 - Prob. 75RE Ch. 8 - Prob. 76RE Ch. 8 - Prob. 77RE Ch. 8 - LotteryNew York has a lottery game called Quick...Ch. 8 - Prob. 79RE Ch. 8 - Prob. 80RE Ch. 8 - Prob. 81RE Ch. 8 - PitThe card game of Pit was introduced by Parker...

Knowledge Booster

The numbers between 100 and 999 which contain exactly one 5 by subtracting the number that contain no 5’s, or three 5’s from the total.

Solution Summary: The author determines the numbers between 100 and 999 which contain exactly one 5 by subtracting the number that contain no 5's from the total.

The numbers between 100 and 999 which contain exactly one 5 by subtracting the number that contain no 5’s, or three 5’s from the total.

The answer to part (a) directly by creating a tree diagram and considering whether the first digit is a 5 or not, then the second digit, and then the third.

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Chapter 8 Solutions