Introductory Combinatorics5th EditionRichard A. Brualdi Publisher: Prentice HallISBN: 9780136020400
Introductory Combinatorics
Solutions for Introductory Combinatorics
Problem 2E:
How many orderings are there for a deck of 52 cards if all the cards of the same suit are together?
Problem 3E:
In how many ways can a poker hand (five cards) be dealt? How many different poker hands are there?
Problem 4E:
How many distinct positive divisors does each of the following numbers have?
34 × 52 × 76 ×...Problem 5E:
Determine the largest power of 10 that is a factor of the following numbers (equivalently, the...Problem 6E:
How many integers greater than 5400 have both of the following properties?
The digits are...Problem 7E:
In how many ways can four men and eight women be seated at a round table if there are to be two...Problem 8E:
In how many ways can six men and six women be seated at a round table if the men and women are to...Problem 9E:
In how many ways can 15 people be seated at a round table if B refuses to sit next to A? What if B...Problem 10E:
A committee of five people is to be chosen from a club that boasts a membership of 10 men and 12...Problem 11E:
How many sets of three integers between 1 and 20 are possible if no two consecutive integers are to...Problem 12E:
A football team of 11 players is to be selected from a set of 15 players, 5 of whom can play only in...Problem 13E:
There are 100 students at a school and three dormitories, A, B, and C, with capacities 25, 35 and...Problem 14E:
A classroom has two rows of eight seats each. There are 14 students, 5 of whom always sit in the...Problem 15E:
At a party there are 15 men and 20 women.
How many ways are there to form 15 couples consisting of...Problem 16E:
Prove that
by using a combinatorial argument and not the values of these numbers as given in...Problem 17E:
In how many ways can six indistinguishable rooks be placed on a 6-by-6 board so that no two rooks...Problem 18E:
In how many ways can two red and four blue rooks be placed on an 8-by-8 board so that no two rooks...Problem 19E:
We are given eight rooks, five of which are red and three of which are blue.
In how many ways can...Problem 20E:
Determine the number of circular permutations of {0, 1, 2, … , 9} in which 0 and 9 are not opposite....Problem 21E:
How many permutations are there of the letters of the word ADDRESSES? How many 8-permutations are...Problem 22E:
A footrace takes place among four runners. If ties are allowed (even all four runners finishing at...Problem 23E:
Bridge is played with four players and an ordinary deck of 52 cards. Each player begins with a hand...Problem 25E:
A ferris wheel has five cars, each containing four seats in a row. There are 20 people ready for a...Problem 26E:
A group of mn people are to be arranged into m teams each with n players.
Determine the number of...Problem 27E:
In how many ways can five indistinguishable rooks be placed on an 8-by-8 chessboard so that no rook...Problem 28E:
A secretary works in a building located nine blocks east and eight blocks north of his home. Every...Problem 30E:
We are to seat five boys, five girls, and one parent in a circular arrangement around a table. In...Problem 37E:
A bakery sells six different kinds of pastry. If the bakery has at least a dozen of each kind, how...Problem 38E:
How many integral solutions of
x1 + x2 + x3 + x4 = 30
satisfy x1 ≥ 2, x2 ≥ 0, x3 ≥ −5, and x4 ≥ 8?
Problem 39E:
There are 20 identical sticks lined up in a row occupying 20 distinct places as follows:
Six of...Problem 40E:
There are n sticks lined up in a row, and k of them are to be chosen.
How many choices are...Problem 41E:
In how many ways can 12 indistinguishable apples and 1 orange be distributed among three children in...Problem 44E:
Prove that the number of ways to distribute n different objects among k children equals kn.
Problem 47E:
There are 2n + 1 identical books to be put in a bookcase with three shelves. In how many ways can...Problem 50E:
In how many ways can five identical rooks be placed on the squares of an 8-by-8 board so that four...Problem 51E:
Consider the multiset {n · a, 1, 2, 3, … , n} of size 2n. Determine the number of its...Problem 52E:
Consider the multiset {n · a, n · b, 1, 2, 3, … , n+1} of size 3n + 1. Determine the number of its...Problem 53E:
Find a one-to-one correspondence between the permutations of the set {1, 2,…, n} and the towers A0 ⊂...Problem 55E:
How many permutations are there of the letters in the words
TRISKAIDEKAPHOBIA (fear of the number...Problem 56E:
What is the probability that a poker hand contains a flush (that is, five cards of the same suit)?
Problem 57E:
What is the probability that a poker hand contains exactly one pair (that is, a poker hand with...Problem 60E:
A bagel store sells six different kinds of bagels. Suppose you choose 15 bagels at random. What is...Problem 61E:
Consider an 9-by-9 board and nine rooks of which five are red and four are blue. Suppose you place...Browse All Chapters of This Textbook
Chapter 1 - What Is Combinatorics?Chapter 2 - Permutations And CombinationsChapter 3 - The Pigeonhole PrincipleChapter 4 - Generating Permutations And CombinationsChapter 5 - The Binomial CoefficientsChapter 6 - The Inclusion-exclusion Principle And ApplicationsChapter 7 - Recurrence Relations And Generating FunctionsChapter 8 - Special Counting SequencesChapter 9 - Systems Of Distinct RepresentativesChapter 10 - Combinatorial Designs
Book Details
This trusted best-seller emphasizes combinatorial ideasndash;including the pigeon-hole principle, counting techniques, permutations and combinations, Poacute;lya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatortial structures (matchings, designs, graphs), and flows in networks. The Fifth Edition clarifies the exposition throughout and adds a wealth of new exercises.Appropriate for one- or two-semester, junior- to senior-level combinatorics courses.
Sample Solutions for this Textbook
We offer sample solutions for Introductory Combinatorics homework problems. See examples below:
To show this, we have to add 3 cases here. Case 1: Assume that one of m and n is even and the second...Procedure used: Multiplication principle: When a task has p outcomes and, no matter what the outcome...Given: The cumulative number of games played on the first n days is denoted by an, where n=1,2,…,77....Algorithm used: Begin with 1←,2←,⋯,n←. While there exists a mobile integer, do the following: (1)...Formula used: The pascal’s triangle formula is: (nk)=n!k!(n−k)!=n(n−1)⋅⋅⋅(n−k+1)k(k−1)⋅⋅⋅1...Suppose the set S={1,2,...,104}. Let A, B, C be the set of integers S that are divisible by 4, 5, 6...Using the mathematical induction and the Fibonacci recurrence. The sequence of numbers...Chapter 8, Problem 1EDefinition used: Let Y be a finite set and A=(A1,A2,…,An) be a family of n subsets of Y. A family...
Definition used: “Let n be a positive integer with n≥2, then Zn={0,1,…,n−1}.” “For any two integers...Definition used: “Two general graphs G=(V,E) and G=(V′,E′) are called isomorphic, provided that...Definition used: Chromatic number: Let G=(V,E) be a graph. A vertex coloring of G is an assignment...The given permutations are, f=(123456642153) and g=(123456356241). Here, (f∘g)(1)=2, (f∘g)(2)=5,...
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