5th Edition

ISBN: 9780357097717

Author: EPP

Publisher: CENGAGE L

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter 9.3, Problem 31ES

Assume that birthdays are equally likely to occur in any one of the 12 months of the year.

a. Given a group of four people, A, B, C, and D, what is the total number of ways in which birth months could be associated with A, B, C, and D? (For instance, A and B might have been born in May, C in September, and D in February. As another example, A might have been born in January, B in June, C in March, and D in October.)

b. How many ways could birth months be associated with A, B, C, and D so that no two people would share the same birth month?

c. How many ways could birth months be associated with A, B, C, and D so that at least two people would share the same birth month?

d. What is the probability that at least two people out of A, B, C, and D share the same birth month?

e. How large must n be so that in any group of n people, the probability that two or more share the same birth month is at least 50%?

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Chapter 9.3, Problem 30ES

Chapter 9.3, Problem 32ES

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Chapter 9 Solutions

DISCRETE MATHEMATICS WITH APPLICATION (

Ch. 9.1 - A sample space of a random process or experiment...Ch. 9.1 - An event in a sample space is .Ch. 9.1 - To compute the probability of an event using the...Ch. 9.1 - Prob. 4TY Ch. 9.1 - Toss two coins 30 times and make a table showing...Ch. 9.1 - In the example of tossing two quarters, what is...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...

Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - Suppose that a coin is tossed three times and the...Ch. 9.1 - Suppose that each child born is equally likely to...Ch. 9.1 - Suppose that on a true/false exam you have no idea...Ch. 9.1 - There people have been exposed to a certain...Ch. 9.1 - Prob. 15ES Ch. 9.1 - Two faces of a six-sided die are painted red, two...Ch. 9.1 - Prob. 17ES Ch. 9.1 - Prob. 18ES Ch. 9.1 - An urn contains two blue balls (denoted B1 and B2)...Ch. 9.1 - Relet to Example 9.1.3. Suppose you are appealing...Ch. 9.1 - Prob. 21ES Ch. 9.1 - a. How many positive three-digit integers are...Ch. 9.1 - Suppose A[1],A[2],A[3],....,A[n] is a...Ch. 9.1 - Suppose A[1],A[2],...,A[n] is a one-dimensional...Ch. 9.1 - Suppose A[1], A[2],…A[n] is a one-dimensional...Ch. 9.1 - Prob. 26ES Ch. 9.1 - What is the 62nd element in the one-dimensional...Ch. 9.1 - If the largest of 56 consecutive integers is 279,...Ch. 9.1 - Prob. 29ES Ch. 9.1 - How many even integers are between 1 and 1,.001?Ch. 9.1 - Prob. 31ES Ch. 9.1 - A certain non-leap year has 365 days, and January...Ch. 9.1 - Prove Theorem 9.1.1. (Let m be any integer and...Ch. 9.2 - The multiplication rule says that if an operation...Ch. 9.2 - A permutation of a set of elements is_________.Ch. 9.2 - Prob. 3TY Ch. 9.2 - Prob. 4TY Ch. 9.2 - Prob. 5TY Ch. 9.2 - Prob. 6TY Ch. 9.2 - Prob. 1ES Ch. 9.2 - Prob. 2ES Ch. 9.2 - Prob. 3ES Ch. 9.2 - Prob. 4ES Ch. 9.2 - Prob. 5ES Ch. 9.2 - One urn contains two black balls (Labeled B1 and...Ch. 9.2 - One urn contains one blue ball (labeled B1) and...Ch. 9.2 - A person buying a personal computer system is...Ch. 9.2 - Suppose there are three roads from city A to city...Ch. 9.2 - Suppose there are three routes from North Point to...Ch. 9.2 - (a)A bit string is a finite sequence of 0’s and...Ch. 9.2 - Hexadecimal numbers are made using the sixteen...Ch. 9.2 - A coin is tossed four times. Each time the result...Ch. 9.2 - Suppose that in a certain stale, all automobile...Ch. 9.2 - A combination lock requires three selections of...Ch. 9.2 - a. How many integers are there from 10 through 99?...Ch. 9.2 - a. How many integers arc there from 1000 through...Ch. 9.2 - The following diagram shows the keypad for an...Ch. 9.2 - Three officers-a president, a treasurer, and a...Ch. 9.2 - Prob. 20ES Ch. 9.2 - Suppose A is a set with m elements and B is a set...Ch. 9.2 - Prob. 22ES Ch. 9.2 - In Section 2.5 we showed how integers can be...Ch. 9.2 - In each of 24—28, determine how many times the...Ch. 9.2 - In each of 24-28, determine how many times...Ch. 9.2 - Prob. 26ES Ch. 9.2 - Prob. 27ES Ch. 9.2 - Prob. 28ES Ch. 9.2 - Consider the numbers 1 through 99,999 in their...Ch. 9.2 - Prob. 30ES Ch. 9.2 - a. If p is a prime number and a is a positive...Ch. 9.2 - (a) How many ways can the letters of the word...Ch. 9.2 - Six people attend the theater together and sit in...Ch. 9.2 - Prob. 34ES Ch. 9.2 - Write all the 2-permutations of {W,X,Y,Z}.Ch. 9.2 - Write all the 3-permutations of {s,t,u,v}.Ch. 9.2 - Evaluate the following quantities. a. P(6,4)b....Ch. 9.2 - a. How many 3-permutations are there of a set of...Ch. 9.2 - a. How many ways can three of the letters of the...Ch. 9.2 - Prove that for every integer n2. P(n+1,3)=n3n Ch. 9.2 - Prob. 41ES Ch. 9.2 - Prob. 42ES Ch. 9.2 - Prob. 43ES Ch. 9.2 - Prove Theorem 9.2.1 by mathematical induction.Ch. 9.2 - Prove Theorem 9.2.2 by mathematical induction.Ch. 9.2 - Prob. 46ES Ch. 9.2 - Prob. 47ES Ch. 9.3 - The addition rule says that if a finite set A...Ch. 9.3 - Prob. 2TY Ch. 9.3 - Prob. 3TY Ch. 9.3 - Prob. 4TY Ch. 9.3 - Prob. 5TY Ch. 9.3 - (a) How many bit string consist of from one...Ch. 9.3 - (a) How many string of hexadecimal digits consist...Ch. 9.3 - (a) How many integers from 1 through 999 do not...Ch. 9.3 - How many arrangements in a row of no more than...Ch. 9.3 - (a) How many five-digit integers (integers from...Ch. 9.3 - In a certain stale, all license plain consist of...Ch. 9.3 - At a certain company, passwords must be from...Ch. 9.3 - In a certain country license plates consist of...Ch. 9.3 - a. Consider the following algorithm segment: for...Ch. 9.3 - A calculator has an eight-digit display and a...Ch. 9.3 - a. How many ways can the letters of the word QUICK...Ch. 9.3 - (a) How many ways can the letters of the word...Ch. 9.3 - A group of eight people are attending the movies...Ch. 9.3 - Prob. 14ES Ch. 9.3 - Prob. 15ES Ch. 9.3 - Prob. 16ES Ch. 9.3 - (a) How many string of four hexadecimal digits do...Ch. 9.3 - Prob. 18ES Ch. 9.3 - A combination lock requires three selections of...Ch. 9.3 - (a) How many integers from 1 through 100,000...Ch. 9.3 - Prob. 21ES Ch. 9.3 - Consider strings of length n over the set {a, b,...Ch. 9.3 - (a) How many integers from 1 through 1,000 are...Ch. 9.3 - (a) How many integers from 1 through 1,000 are...Ch. 9.3 - Prob. 25ES Ch. 9.3 - Prob. 26ES Ch. 9.3 - For each integer n0 . let akbe the number of bit...Ch. 9.3 - Prob. 28ES Ch. 9.3 - Refer to Example 9.3.5. Write the following IP...Ch. 9.3 - A now in a classroom has n seats. Let sn be the...Ch. 9.3 - Assume that birthdays are equally likely to occur...Ch. 9.3 - Assuming that all years have 365 days and all...Ch. 9.3 - A college conducted a survey to explore the...Ch. 9.3 - A study was done to determine the efficacy of...Ch. 9.3 - Prob. 35ES Ch. 9.3 - Prob. 36ES Ch. 9.3 - Prob. 37ES Ch. 9.3 - Prob. 38ES Ch. 9.3 - Prob. 39ES Ch. 9.3 - Prob. 40ES Ch. 9.3 - For 40 and 41, use the definition of the Euler phi...Ch. 9.3 - Prob. 42ES Ch. 9.3 - Prob. 43ES Ch. 9.3 - Prob. 44ES Ch. 9.3 - Prob. 45ES Ch. 9.3 - Prob. 46ES Ch. 9.3 - Prob. 47ES Ch. 9.3 - Prob. 48ES Ch. 9.3 - Prob. 49ES Ch. 9.4 - The pigeonhole principle states that_______Ch. 9.4 - The generalized pigeonhole principle states that...Ch. 9.4 - If X and Y are finite sets and f is a function...Ch. 9.4 - A small town has only 500 residents. Must there be...Ch. 9.4 - In a group of 700 people, must there be 2 who have...Ch. 9.4 - (a) Given any set of four integers, must there be...Ch. 9.4 - (a) Given any set of seven integers, must there be...Ch. 9.4 - Let S={3,4,5,6,7,8,9,10,11,12} . Suppose six...Ch. 9.4 - Let T={1,2,3,4,5,6,7,8,9}. Suppose five integers...Ch. 9.4 - (a) If seven integers are chosen from between 1...Ch. 9.4 - If n+1 integers are from the set {1,2,3,...2n}....Ch. 9.4 - If n+1 integers are chosen from the set...Ch. 9.4 - Prob. 12ES Ch. 9.4 - Suppose six pairs of similar-looking boots are...Ch. 9.4 - Prob. 14ES Ch. 9.4 - If n is a positive integer, how many integers from...Ch. 9.4 - How many integer from 1 through 100 must you pick...Ch. 9.4 - Prob. 17ES Ch. 9.4 - How many integers must you pick in order to be...Ch. 9.4 - How many integers from 100 through 999 must you...Ch. 9.4 - Prob. 20ES Ch. 9.4 - When 683/1493 is written as a decimal what is the...Ch. 9.4 - Prob. 22ES Ch. 9.4 - Prob. 23ES Ch. 9.4 - Show that within any set of thirteen integers...Ch. 9.4 - Prob. 25ES Ch. 9.4 - Prob. 26ES Ch. 9.4 - In a group of 2,000 people, must at least 5 have...Ch. 9.4 - A programmer writes 500 lines of computer code in...Ch. 9.4 - A certain collage class has 40 students. All the...Ch. 9.4 - A penny collection contains twelve 1967 pennies,...Ch. 9.4 - A group of 15 exeutives are to share 5 assistants....Ch. 9.4 - Prob. 32ES Ch. 9.4 - Prob. 33ES Ch. 9.4 - Let S be a set of ten integers chosen from 1...Ch. 9.4 - Prob. 35ES Ch. 9.4 - Show that if 101 integers are chosen from 1 to 200...Ch. 9.4 - a. Suppose a1,a2,...,an is a sequence of n...Ch. 9.4 - Prob. 38ES Ch. 9.4 - What is the largest number of elements that a set...Ch. 9.4 - Prob. 40ES Ch. 9.5 - Prob. 1TY Ch. 9.5 - The number of r-combinations of a set of n...Ch. 9.5 - Prob. 3TY Ch. 9.5 - Prob. 4TY Ch. 9.5 - Prob. 5TY Ch. 9.5 - Prob. 1ES Ch. 9.5 - Prob. 2ES Ch. 9.5 - Prob. 3ES Ch. 9.5 - Write an equation relating P(8,3) and (38) .Ch. 9.5 - Use Theorem 9.5.1 to compute each of the...Ch. 9.5 - A student council consists of 15 students. a. In...Ch. 9.5 - A computer programming team has 13 members. a. How...Ch. 9.5 - An instructor gives an exam with fourteen...Ch. 9.5 - A club is cosidering changing its bylaws. In an...Ch. 9.5 - Two new drugs -ire to be tested using a group of...Ch. 9.5 - Refer to Example 9.5.9. For each poker holding...Ch. 9.5 - How many pairs of two distinct integers chosen...Ch. 9.5 - A coin is tossed ten times. In each case the...Ch. 9.5 - (a) How many 16-bit strings contain exactly seven...Ch. 9.5 - (a) How many even integer are in the set...Ch. 9.5 - Suppose that three microchips in a production run...Ch. 9.5 - Ten points Libeled A. B. C. D. E. F. G. H, I. J...Ch. 9.5 - Prob. 18ES Ch. 9.5 - (a) How many distinguishable ways can the letters...Ch. 9.5 - a. How man distinguishable ways can the letters...Ch. 9.5 - In Morse code, symbols are represented by...Ch. 9.5 - Each symbol in the Braile code is represented by a...Ch. 9.5 - On an 88 chessboard, a rook is allowed to move any...Ch. 9.5 - The number 42 has the prime factorization 237 ....Ch. 9.5 - a. How many one-of-one functions ant there from a...Ch. 9.5 - a. How many onto functions are there from a set...Ch. 9.5 - Let A be a set with eight elements. How many...Ch. 9.5 - A student council consists of three freshmen, four...Ch. 9.5 - Prob. 29ES Ch. 9.5 - Prob. 30ES Ch. 9.6 - Given a set X={x1,x1,,xn} , an r-combination with...Ch. 9.6 - Prob. 2TY Ch. 9.6 - Prob. 3TY Ch. 9.6 - (a) According to Theorem 9.6.1, how many...Ch. 9.6 - (a) According to Theorem 9.6.1, how many multisets...Ch. 9.6 - A bakery produces six different kinds of pastry,...Ch. 9.6 - A camera shop stocks eight different types of...Ch. 9.6 - If n is a positive integer, how many 4-tuples of...Ch. 9.6 - If n is a positive integer, how many 5-tuples of...Ch. 9.6 - Prob. 7ES Ch. 9.6 - Prob. 8ES Ch. 9.6 - In 8 and 9, how many times will the innermost loop...Ch. 9.6 - Prob. 10ES Ch. 9.6 - Prob. 11ES Ch. 9.6 - Prob. 12ES Ch. 9.6 - In 10-14, find how many solutions there are to the...Ch. 9.6 - In 10-14, find how many solutions there are to the...Ch. 9.6 - Prob. 15ES Ch. 9.6 - Consider the situation in Example 9.6.2. a....Ch. 9.6 - a. A store sells 8 colors of balloons with at...Ch. 9.6 - A large pile of coins consists of penruey nickels,...Ch. 9.6 - Suppose the bakery in exercise 3 has at least...Ch. 9.6 - Suppose the camera shop in exercise 4 can obtain...Ch. 9.6 - Prob. 21ES Ch. 9.7 - If n and r are nonnegative integers with rn , then...Ch. 9.7 - Prob. 2TY Ch. 9.7 - Prob. 3TY Ch. 9.7 - Prob. 4TY Ch. 9.7 - Prob. 5TY Ch. 9.7 - Prob. 6TY Ch. 9.7 - Prob. 7TY Ch. 9.7 - Prob. 1ES Ch. 9.7 - Prob. 2ES Ch. 9.7 - Prob. 3ES Ch. 9.7 - Prob. 4ES Ch. 9.7 - Prob. 5ES Ch. 9.7 - Prob. 6ES Ch. 9.7 - Prob. 7ES Ch. 9.7 - Prob. 8ES Ch. 9.7 - Prob. 9ES Ch. 9.7 - (a) Use Pascal’s triangle given in Table 9.7.1 to...Ch. 9.7 - Prob. 11ES Ch. 9.7 - Use Pascal’s formula repeatedly to derive a...Ch. 9.7 - Use Pascal’s formula to prove by mathematical...Ch. 9.7 - Prob. 14ES Ch. 9.7 - Prove the following generalization of exercise 13:...Ch. 9.7 - Prob. 16ES Ch. 9.7 - Prove that for every integer n0 ,...Ch. 9.7 - Prob. 18ES Ch. 9.7 - Prob. 19ES Ch. 9.7 - Prob. 20ES Ch. 9.7 - Prob. 21ES Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Prob. 25ES Ch. 9.7 - Prob. 26ES Ch. 9.7 - Prob. 27ES Ch. 9.7 - Prob. 28ES Ch. 9.7 - Prob. 29ES Ch. 9.7 - Prob. 30ES Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - Prob. 33ES Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - Prob. 35ES Ch. 9.7 - For every integer n1 ,...Ch. 9.7 - Prob. 37ES Ch. 9.7 - Prob. 38ES Ch. 9.7 - Prob. 39ES Ch. 9.7 - Prob. 40ES Ch. 9.7 - Prob. 41ES Ch. 9.7 - Prob. 42ES Ch. 9.7 - Prob. 43ES Ch. 9.7 - Prob. 44ES Ch. 9.7 - Prob. 45ES Ch. 9.7 - Prob. 46ES Ch. 9.7 - Prob. 47ES Ch. 9.7 - Prob. 48ES Ch. 9.7 - Prob. 49ES Ch. 9.7 - Prob. 50ES Ch. 9.7 - Express each of the sums in 43—54 in closed form...Ch. 9.7 - Prob. 52ES Ch. 9.7 - Prob. 53ES Ch. 9.7 - Prob. 54ES Ch. 9.7 - Prob. 55ES Ch. 9.8 - If A is an event in a sample space S,P(A) can...Ch. 9.8 - Prob. 2TY Ch. 9.8 - Prob. 3TY Ch. 9.8 - Prob. 4TY Ch. 9.8 - Prob. 5TY Ch. 9.8 - Prob. 1ES Ch. 9.8 - Prob. 2ES Ch. 9.8 - Prob. 3ES Ch. 9.8 - Prob. 4ES Ch. 9.8 - Prob. 5ES Ch. 9.8 - Prob. 6ES Ch. 9.8 - Prob. 7ES Ch. 9.8 - Prob. 8ES Ch. 9.8 - Let A and B be events in a sample space S, and let...Ch. 9.8 - Prob. 10ES Ch. 9.8 - Prob. 11ES Ch. 9.8 - Prob. 12ES Ch. 9.8 - Prob. 13ES Ch. 9.8 - A lottery game offers $2 million to the grand...Ch. 9.8 - A company offers a raffle whose grand prize is a...Ch. 9.8 - An urn contains four balls numbered 2, 2, 5, and...Ch. 9.8 - Prob. 17ES Ch. 9.8 - An urn contains five balls numbered 1,2,2,8, and...Ch. 9.8 - Prob. 19ES Ch. 9.8 - Suppose a person offers to play a game with you....Ch. 9.8 - Prob. 21ES Ch. 9.8 - Prob. 22ES Ch. 9.8 - Prob. 23ES Ch. 9.9 - Prob. 1TY Ch. 9.9 - Prob. 2TY Ch. 9.9 - Prob. 3TY Ch. 9.9 - Prob. 4TY Ch. 9.9 - Prob. 1ES Ch. 9.9 - Prob. 2ES Ch. 9.9 - Prob. 3ES Ch. 9.9 - Prob. 4ES Ch. 9.9 - Suppose that A and B are events in a sample space...Ch. 9.9 - An urn contains 25 red balls and 15 blue balls....Ch. 9.9 - Prob. 7ES Ch. 9.9 - A pool of 10 semifinalists for a job consists of 7...Ch. 9.9 - Prob. 9ES Ch. 9.9 - Prob. 10ES Ch. 9.9 - One urn contains 12 blue balls and 7 white balls,...Ch. 9.9 - Redo exercise 11 assuming that the first urn...Ch. 9.9 - Prob. 13ES Ch. 9.9 - Prob. 14ES Ch. 9.9 - Prob. 15ES Ch. 9.9 - Three different supplier.-X, Y. and Z-provide...Ch. 9.9 - Prob. 17ES Ch. 9.9 - Prob. 18ES Ch. 9.9 - Prob. 19ES Ch. 9.9 - Prob. 20ES Ch. 9.9 - Prob. 21ES Ch. 9.9 - Prob. 22ES Ch. 9.9 - Prob. 23ES Ch. 9.9 - Prob. 24ES Ch. 9.9 - A coin is loaded so that the probability of heads...Ch. 9.9 - Describe a sample space and events A,B, and C,...Ch. 9.9 - Prob. 27ES Ch. 9.9 - Prob. 28ES Ch. 9.9 - Suppose that ten items are chosen at random from a...Ch. 9.9 - Suppose the probability of a false positive result...Ch. 9.9 - Prob. 31ES Ch. 9.9 - Prob. 32ES Ch. 9.9 - Prob. 33ES Ch. 9.9 - Prob. 34ES

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Solution Summary: The author calculates the total number of ways in which birth months could be associated with A, B, C and D.

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