1 The Foundations: Logic And Proofs 2 Basic Structures: Sets, Functions, Sequences, Sums, And Matrices 3 Algorithms 4 Number Theory And Cryptography 5 Induction And Recursion 6 Counting 7 Discrete Probability 8 Advanced Counting Techniques 9 Relations 10 Graphs 11 Trees 12 Boolean Algebra 13 Modeling Computation A Appendices expand_more
6.1 The Basics Of Counting 6.2 The Pigeonhole Principle 6.3 Permutations And Combinations 6.4 Binomial Coefficients And Identities 6.5 Generalized Permutations And Combinations 6.6 Generating Permutations And Combinations Chapter Questions expand_more
Problem 1E: There are 18 mathematics majors and 325 computer science majors at a college, In how many ways can... Problem 2E: An office building contains 27 floors and has 37 offices on each floor. How many offices are in the... Problem 3E: A multiple-choice test contains 10 questions. There are four possible answers for each question. In... Problem 4E: A particular of shirt comes in 12 colors, has a male version and a female version, and comes in... Problem 5E: Six different fly from New York to Denver and seven fly from Denver to San Francisco. How many... Problem 6E: There are four major auto routes from Boston to Detroit to Los Angeles. How many major auto routes... Problem 7E: How many different three-letter initials can people have? Problem 8E: How many different three-letter initials with none of the letters repeated can people have? Problem 9E: How many different three-letter initials are there that begin with an A? Problem 10E: How many bit strings are there of length eight? Problem 11E: How many bit strings of length ten both begin and end yvith a1? Problem 12E: How many bit strings are there of length six or less, not counting the empty string? Problem 13E: How many bit strings with length not exceeding n, where n is a positive integer, consist entirely of... Problem 14E: How many bit strings of lengthn,wherenis a positive integer, start and end with is? Problem 15E: How many strings are there of lowercase letters of length four or less, not counting the empty... Problem 16E: How many strings are there of four lowercase letters that have the letter x in them? Problem 17E: How many strings of five ASCII characters @ (“at” sign) at least once? [Note: There are 128... Problem 18E: How many 5-element DNA sequences end with A? start with T and end with G? c) contain only A and T?... Problem 19E: lg.How many 6-element RNA sequences Do not contain U? end with GU? start with C? d)contain onlyAor... Problem 20E: How many positive integers between 5 and 31 are divisible by 3? Which integers are these? are... Problem 21E: How many positive integers between 50 and 100 are divisible by 7? Which integers are these? are... Problem 22E: How many positive integers less than 1000 are divisible by 7? are divisible by 7 but not by11? are... Problem 23E: How many positive integers between 100 and 999 inclusive are divisible by 7? are odd? have the same... Problem 24E: How many positive integers between 1000 and 9999 inclusive are divisible by 9? are even? have... Problem 25E: How many strings of three decimal digits do not contain the same digit three times? begin with an... Problem 26E: How many strings of four decimal digits do not contain the same digit twice? end with an even digit?... Problem 27E Problem 28E: How many license, plates can be made using either three digits followed by three uppercase English... Problem 29E: How many license plates can be made using either two uppercase English letters followed by four... Problem 30E: How many license plates can be made using either three upper case English letters followed by three... Problem 31E: How many license plates can be made using either two or three uppercase English letters followed by... Problem 32E: How many strings of eight uppercase English letters are there if letters can b e repeated? if no... Problem 33E: How many strings of eight English letters are there that contain no vowels, if letters can be... Problem 34E Problem 35E: How many one-to-one functions are there from a set with five elements to sets with the following... Problem 36E: How many functions are there from the set {1,2,n}, wherenis a positive integer, to the set {o, 1}? Problem 37E Problem 38E: How many partial functions (seeSection 2.3)are there from a set with five elements to sets with each... Problem 39E Problem 40E Problem 41E Problem 42E: How many 4-element DNA sequences do not contain the base T? contain the sequence ACG? c) contain all... Problem 43E: How many 4-eJement RNA sequenoes contain the base U? do not contain the sequence CUG? do not contain... Problem 44E: On each of the 22 work days in a particular month, every employee of a start-up venture was sent to... Problem 45E: At a large university, 434 freshman, 883 sophomores, and 43 juniors are enrolled in an introductory... Problem 46E Problem 47E: How many ways are there to seat six people around a circular table where two seatings are considered... Problem 48E: In how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10... Problem 49E: In how many ways can a photographer at a wedding arrange six people in a row, including the bride... Problem 50E: How many bit strings of length seven either begin ivith two os or end with three is? Problem 51E Problem 52E: How many bit strings of length 10 contain either five consecutive os or five consecutive is? Problem 53E: How many bit strings of length eight contain either three consecutive os or four consecutive 1s? Problem 54E: ... Problem 55E Problem 56E Problem 57E: Suppose that a password for a computer system must have at least 8, but no more than 12, characters,... Problem 58E: The name, of a variable in the C programming language is a string that can contain uppercase... Problem 59E: The name of a variable in the JAVA programming language is a string of beta 1 and 65,535 characters,... Problem 60E: 6o, The International Telecommunications Union (ITU) specifies that a telephone number must consist... Problem 61E Problem 62E: A key in the Vigenere cryptosystem is a string of English letters, where the case of the letters... Problem 63E Problem 64E: Suppose that P and q are prime numbers and than n = pq. Use the principle of inclusion-exclusion to... Problem 65E: Use the principle of inclusion-exclusion to find the number of positive integers less than 1,000,000... Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E: Determine the number of matches played in a singleelimination tournament with n players, where for... Problem 73E Problem 74E: *74-Use the product rule to show that there are 22 different truth tables for propositions... Problem 75E Problem 76E: Use mathematical induction to prove the product rule formtasks from the product rule for two tasks. Problem 77E Problem 78E format_list_bulleted