To determine To evaluate: The probability that 3 consecutive numbers n , n + 1 and n + 2 are picked and no pairs of consecutive numbers other than n , n + 1 and n + 1 , n + 2 are picked. Explanation Given that in the Illinois State Lotto game 6 of the integers 1 , 2 , … , 54 are picked to be the winning numbers. The total number of ways of selecting the numbers can be done in C ( 54 , 6 ) ways. Among the given numbers, { 1 , 2 , 3 } is a pair, { 2 , 3 , 4 } is a pair and so on { 52 , 53 , 54 } is a pair. Thus, there are n − 2 pairs of three consecutive integers. The remaining numbers when the first or the last pair is chosen will be { 4 , 5 , 6 , … , 54 } . Among the 51 numbers the can be done in C ( n − 2 , 3 ) = C ( 49 , 3 ) ways

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 8.5, Problem 36E

To determine

To evaluate: The probability that 3 consecutive numbers n,n+1 and n+2 are picked and no pairs of consecutive numbers other than n,n+1 and n+1,n+2 are picked.

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Chapter 8.5, Problem 35E

Chapter 8.6, Problem 1E

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Chapter 8 Solutions

Discrete Mathematics

Ch. 8.1 - Evaluate the numbers in Exercises 1-12. C(5, 3) Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. C(12, 7) Ch. 8.1 - Prob. 5E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Prob. 7E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Prob. 9E Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...

Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...Ch. 8.1 - Evaluate the numbers in Exercises 1-12. the...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 - Prob. 21E Ch. 8.1 - Prob. 22E 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. 8.2 - How many people must there be in order to assure...Ch. 8.2 - If a committee varies its meeting days, how many...Ch. 8.2 - Prob. 3E Ch. 8.2 - How many words must be chosen in order to assure...Ch. 8.2 - Prob. 5E Ch. 8.2 - If there are 6 sections of Discrete Math with a...Ch. 8.2 - Prob. 7E Ch. 8.2 - A sociologist intends to send a questionnaire to...Ch. 8.2 - Prob. 9E Ch. 8.2 - How many different pizzas can be ordered if a...Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - A restaurant offers a choice of 3 green vegetables...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 - How many 8-bit strings begin with 010 or end with...Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prove that in any nonempty list of n integers (not...Ch. 8.2 - Prob. 35E Ch. 8.2 - Suppose that there are 15 identical copies of The...Ch. 8.3 - Evaluate the numbers in Exercises 1-12. 1. C(6,...Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Evaluate the numbers in Exercises 1-12. 4. C(8,...Ch. 8.3 - Evaluate the numbers in Exercises 1-12. 5. P(4,...Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Evaluate the numbers in Exercises 1-12. 8. P(12,...Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Evaluate the numbers in Exercises 1-12. 12. P(n,...Ch. 8.3 - Prob. 13E Ch. 8.3 - How many different arrangements are there of the...Ch. 8.3 - Prob. 15E Ch. 8.3 - How many different ways are there of selecting...Ch. 8.3 - Prob. 17E Ch. 8.3 - How many different 16-bit strings contain exactly...Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E 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 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.4 - How many distinct arrangements of the letters in...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - How many different assortments of 6 boxes of...Ch. 8.4 - Prob. 7E Ch. 8.4 - How many different boxes containing 10 wedges of...Ch. 8.4 - Prob. 9E Ch. 8.4 - In how many different ways can 15 distinct books...Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - In how many different ways can 6 identical sticks...Ch. 8.4 - A father has 10 identical life insurance policies....Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - In how many different ways can 8 identical...Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 26E Ch. 8.4 - How many positive integers less than 10,000 are...Ch. 8.4 - How many distinct arrangements are there of two...Ch. 8.4 - How many positive integers less than 1,000,000 are...Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E 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 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - What is the probability that a randomly chosen...Ch. 8.5 - Prob. 20E Ch. 8.5 - Three $ 10 bills, four $5 bills, and six $1 bills...Ch. 8.5 - If a 5-member committee is selected at random from...Ch. 8.5 - Suppose that we randomly distribute 5 distinct...Ch. 8.5 - If 10 quarters are distributed at random to 4...Ch. 8.5 - Exactly 4 of 20 microcomputer diskettes are...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - In Exercises 31–34, compute the probability of...Ch. 8.5 - A file contains 25 accounts numbered 1–25. If 5 of...Ch. 8.5 - In the Illinois State Lotto game, 6 of the...Ch. 8.6 - In a survey of moviegoers it was found that 33...Ch. 8.6 - Among a group of children, 88 liked pizza and 27...Ch. 8.6 - Among the 318 members of a local union, 127 liked...Ch. 8.6 - In a particular dormitory, there are 350 college...Ch. 8.6 - From a group of 650 residents of a city, the...Ch. 8.6 - In tabulating the 5681 responses to a...Ch. 8.6 - The following data were obtained from the...Ch. 8.6 - The following information was found about the...Ch. 8.6 - Eight married couples came to a bridge party. Each...Ch. 8.6 - List all the derangements of 1, 2, 3, 4. Ch. 8.6 - While taking a 6-week summer math class, Alison...Ch. 8.6 - How many sequences of five digits (0–9) contain at...Ch. 8.6 - For the following graph, determine the number of...Ch. 8.6 - If three married couples are seated randomly in...Ch. 8.6 - How many positive integers less than 101 are...Ch. 8.6 - How many sequences of six digits (0–9) contain at...Ch. 8.6 - At Brokaw Hospital, six babies were born to six...Ch. 8.6 - In how many ways can four married couples be...Ch. 8.6 - How many arrangements of the numbers 1, 1, 2, 2,...Ch. 8.6 - How many five-card poker hands contain at least...Ch. 8.6 - How many of the functions with domain {5, 6, 7, 8,...Ch. 8.6 - How many nonnegative integer solutions of x1 + x2...Ch. 8.6 - Suppose that five balls numbered 1, 2, 3, 4, and 5...Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - For nonnegative integers n and m, define S(n, m)...Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.7 - Prob. 1E Ch. 8.7 - Prob. 2E Ch. 8.7 - Prob. 3E Ch. 8.7 - Prob. 4E Ch. 8.7 - Prob. 5E Ch. 8.7 - Prob. 6E Ch. 8.7 - Prob. 7E Ch. 8.7 - Prob. 8E Ch. 8.7 - In Exercises 7-18, determine the successor of...Ch. 8.7 - Prob. 10E Ch. 8.7 - Prob. 11E Ch. 8.7 - Prob. 12E Ch. 8.7 - Prob. 13E Ch. 8.7 - Prob. 14E Ch. 8.7 - Prob. 15E Ch. 8.7 - Prob. 16E Ch. 8.7 - Prob. 17E Ch. 8.7 - Prob. 18E Ch. 8.7 - Prob. 19E Ch. 8.7 - Prob. 20E Ch. 8.7 - Prob. 21E Ch. 8.7 - Prob. 22E Ch. 8.7 - Prob. 23E Ch. 8.7 - Prob. 24E Ch. 8.7 - Prob. 25E Ch. 8.7 - Prob. 26E Ch. 8.7 - Prob. 27E Ch. 8.7 - Prob. 28E Ch. 8.7 - Prob. 29E Ch. 8.7 - Prob. 30E Ch. 8.7 - Prob. 31E Ch. 8.7 - Prob. 32E Ch. 8 - Prob. 1SE Ch. 8 - Prob. 2SE Ch. 8 - Prob. 3SE Ch. 8 - Prob. 4SE Ch. 8 - Prob. 5SE Ch. 8 - Prob. 6SE Ch. 8 - Prob. 7SE Ch. 8 - Prob. 8SE Ch. 8 - Prob. 9SE Ch. 8 - Prob. 10SE Ch. 8 - Prob. 11SE Ch. 8 - Prob. 12SE Ch. 8 - Prob. 13SE Ch. 8 - Prob. 14SE Ch. 8 - Prob. 15SE Ch. 8 - Prob. 16SE Ch. 8 - Prob. 17SE Ch. 8 - How many integers between 1500 and 8000...Ch. 8 - Prob. 19SE Ch. 8 - Prob. 20SE Ch. 8 - Prob. 21SE Ch. 8 - Prob. 22SE Ch. 8 - Prob. 23SE Ch. 8 - Prob. 24SE Ch. 8 - Prob. 25SE Ch. 8 - Prob. 26SE Ch. 8 - Prob. 27SE Ch. 8 - Prob. 28SE Ch. 8 - Prob. 29SE Ch. 8 - Prob. 30SE Ch. 8 - Prob. 31SE Ch. 8 - Prob. 32SE Ch. 8 - Prob. 33SE Ch. 8 - Prob. 34SE Ch. 8 - Prob. 35SE Ch. 8 - Prob. 36SE Ch. 8 - Prob. 37SE Ch. 8 - Prob. 38SE Ch. 8 - Prob. 39SE Ch. 8 - Prob. 41SE Ch. 8 - Prob. 42SE Ch. 8 - Prob. 43SE Ch. 8 - Prob. 44SE Ch. 8 - Prob. 45SE Ch. 8 - Prob. 46SE Ch. 8 - Prob. 47SE Ch. 8 - Prob. 49SE Ch. 8 - Prob. 50SE Ch. 8 - Prob. 51SE Ch. 8 - Prob. 52SE Ch. 8 - Prob. 53SE Ch. 8 - Prob. 56SE Ch. 8 - Prob. 57SE Ch. 8 - Prob. 3CP Ch. 8 - Prob. 4CP

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