A First Course in Probability (10th Edi...10th EditionSheldon Ross Publisher: PEARSONISBN: 9780134753119
A First Course in Probability (10th Edi...
Solutions for A First Course in Probability (10th Edition)
Problem 1.1P:
a. How many different 7-place license plates are possible if the first 2 places are for letters and...Problem 1.2P:
How many outcome sequences are possible ten a die is rolled four times, where we say, for instance,...Problem 1.3P:
Twenty workers are to be assigned to 20 different jobs, one to each job. How many different...Problem 1.4P:
John, Jim, Jay, and Jack have formed a band consisting of 4 instruments if each of the boys can play...Problem 1.5P:
For years, telephone area codes in the United States and Canada consisted of a sequence of three...Problem 1.6P:
A well-known nursery rhyme starts as follows: As I was going to St. Ives I met a man with 7 wives....Problem 1.7P:
a. In how many ways can 3 boys and 3 girls sit in a row? b. In how many ways can 3 boys and 3 girls...Problem 1.8P:
When all letters are used, how many different letter arrangements can be made from the letters a....Problem 1.9P:
A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts...Problem 1.10P:
In how many ways can 8 people be seated in a row if a. there are no restrictions on the seating...Problem 1.11P:
In how many ways can 3 novels. 2 mathematics books, and 1 chemistry book be arranged on a bookshelf...Problem 1.12P:
How many 3 digit numbers zyz, with x, y, z all ranging from 0 to9 have at least 2 of their digits...Problem 1.13P:
How many different letter permutations, of any length, can be made using the letters M 0 T T 0. (For...Problem 1.14P:
Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to...Problem 1.15P:
Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take...Problem 1.16P:
How many 5-card poker hands are there?Problem 1.17P:
A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women...Problem 1.18P:
A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How...Problem 1.19P:
Seven different gifts are to be distributed among 10 children. How many distinct results are...Problem 1.20P:
A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from...Problem 1.21P:
From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How...Problem 1.22P:
A person has 8 friends, of whom S will be invited to a party. a. How many choices are there if 2 of...Problem 1.23P:
Consider the grid of points shown at the top of the next column. Suppose that, starting at the point...Problem 1.24P:
In Problem 23, how many different paths are there from A to B that go through the point circled in...Problem 1.25P:
A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3...Problem 1.26P:
Show k=0n(nk)2k=3n Simplify k=0n(nk)xkProblem 1.27P:
Expand (3x2+y)5.Problem 1.28P:
The game of bridge is played by 4 players, each of w1om is dealt 13 cards. How many bridge deals are...Problem 1.29P:
Expand (x1+2x2+3x3)4.Problem 1.30P:
If 12 people are to be divided into 3 committees of respective sizes 3, 4, and 5, how many divisions...Problem 1.31P:
If 8 new teachers are to be divided among 4 schools, how many divisions are possible? What if each...Problem 1.32P:
Ten weight lifters are competing in a team weight-lifting contest. Of the lifters, 3 are from the...Problem 1.33P:
Delegates from 10 countries, including Russia, France, England, and the United States, are to be...Problem 1.34P:
If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? How...Problem 1.35P:
An elevator starts at the basement with 8 people (not including the elevator operator) and...Problem 1.36P:
We have 520.000 that must be invested among 4 possible opportunities. Each investment must be...Problem 1.37P:
Suppose that 10 fish are caught at a lake that contains 5 distinct types of fish. a. How many...Problem 1.2TE:
Two experiments are to be performed. The first can result in any one of m possible outcomes. If the...Problem 1.3TE:
In how many ways can r objects be selected from a set of n objects if the order of selection is...Problem 1.4TE:
There are (nr) different linear arrangements of n balls of which r are black and nr are white. Give...Problem 1.5TE:
Determine the number of vectors (x1,...,xn), such that each x1 is either 0 or 1 andi=1nxiKProblem 1.6TE:
How many vectors x1,...,xk are there for which each xi is a positive integer such that1xin and...Problem 1.7TE:
Give an analytic proof of Equation (4.1).Problem 1.8TE:
Prove that (n+mr)=(n0)(mr)+(n1)(mr1)+...+(nr)(m0) Hint: Consider a group of n men and m women. How...Problem 1.9TE:
Use Theoretical Exercise 8 I to prove that (2nn)=k=0n(nk)2Problem 1.10TE:
From a group of n people, suppose that we want to choose a committee of k,kn, one of whom is to be...Problem 1.11TE:
The following identity is known as Fermats combinatorial identity:(nk)=i=kn(i1k1)nk Give a...Problem 1.12TE:
Consider the following combinatorial identity: k=0nk(nk)=n2n1 a. Present a combinatorial argument...Problem 1.14TE:
From a set of n people, a committee of size j is to be chosen, and from this committee, a...Problem 1.15TE:
Let Hn(n) be the number of vectors x1,...,xk for which each xi is a positive integer satisfying 1xin...Problem 1.16TE:
Consider a tournament of n contestants in which the outcome is an ordering of these contestants,...Problem 1.17TE:
Present a combinatorial explanation of why (nr)=(nr,nr)Problem 1.18TE:
Argue that(nn1,n2,...,nr)=(n1n11,n2,...,nr)+(nn1,n21,...,nr)+...+(nn1,n2,...,nr1) Hint: Use an...Problem 1.19TE:
Prove the multinomial theorem.Problem 1.20TE:
In how many ways can n identical balls be distributed into r urns so that the ith urn contains at...Problem 1.21TE:
Argue that there are exactly (rk)(n1nr+k) solutions of x1+x2+...+xr=n for which exactly k of the xi...Problem 1.23TE:
Determine the number of vectors (xi,...,xn) such that each xi, is a nonnegative integer and i=1nxik.Problem 1.1STPE:
How many different linear arrangements are there of the letters A, B, C, D, E, F for which a. A and...Problem 1.2STPE:
If 4 Americans, 3 French people, and 3 British people are to be seated in a row, how many seating...Problem 1.3STPE:
A president. treasurer, and secretary. all different, are to be chosen from a club onsisting of 10...Problem 1.4STPE:
A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many...Problem 1.5STPE:
In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts...Problem 1.6STPE:
How many different 7-place license plates are possible mien 3 of the entries are letters and 4 are...Problem 1.7STPE:
Give a combinatorial explanation of the identity(nr)=(nnr)Problem 1.8STPE:
Consider n-digit numbers where each digit is one of the 10 integers 0,1, ... ,9. How many such...Problem 1.9STPE:
Consider three classes, each consisting of n students. From this group of 3n students, a group of 3...Problem 1.10STPE:
How many 5-digit numbers can be formed from the integers 1,2,... ,9 if no digit can appear more than...Problem 1.11STPE:
From 10 married couples, we want to select a group of 6 people that is not allowed to contain a...Problem 1.12STPE:
A committee of 6 people is to be chosen from a group consisting of 7 men and 8 women. If the...Problem 1.13STPE:
An art collection on auction consisted of 4 Dalis, 5 van Goghs. and 6 Picassos, At the auction were...Problem 1.15STPE:
A total of n students are enrolled in a review course for the actuarial examination in probability....Problem 1.17STPE:
Give an analytic verification of (n2)=(k2)+k(nk)+(n+k2),1kn. Now, give a combinatorial argument for...Problem 1.18STPE:
In a certain community, there are 3 families consisting of a single parent and 1 child, 3 families...Problem 1.19STPE:
If there are no restrictions on where the digits and letters are placed, how many 8-place license...Problem 1.20STPE:
Verify the identityx1+...+xr=n,xi0n!x1!x2!...xr!=rn a. by a combinatorial argument that first notes...Problem 1.21STPE:
Simplify n(n2)+(n3)...+(1)n+1(nn)Browse All Chapters of This Textbook
Chapter 1 - Combinatorial AnalysisChapter 2 - Axioms Of ProbabilityChapter 3 - Conditional Probability And IndependenceChapter 4 - Random VariablesChapter 5 - Continuous Random VariablesChapter 6 - Jointly Distributed Random VariablesChapter 7 - Properties Of ExpectationChapter 8 - Limit TheoremsChapter 9 - Additional Topics In ProbabilityChapter 10 - Simulation
Sample Solutions for this Textbook
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More Editions of This Book
Corresponding editions of this textbook are also available below:
EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 9780321926678
A First Course In Probability
9th Edition
ISBN: 9789332519077
EBK A FIRST COURSE IN PROBABILITY
9th Edition
ISBN: 8220101467447
A First Course in Probability
9th Edition
ISBN: 9780321794772
A First Course In Probability
5th Edition
ISBN: 9780137463145
A First Course in Probability
8th Edition
ISBN: 9780136033134
A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
FIRST COURSE IN PROBABILITY (LOOSELEAF)
10th Edition
ISBN: 9780134753751
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
A Second Course in Probability
7th Edition
ISBN: 9780979570407
First Course In Probability, A (7th Edition)
7th Edition
ISBN: 9780131856622
A First Course In Probability (6th Edition)
6th Edition
ISBN: 9780130338518
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