Homework Help is Here – Start Your Trial Now!
Math
Algebra
(a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with 8 elements. So the answer is 40,320 (b) How many ways can the letters of the word ANCESTOR be arranged in a row if A and N must remain together (in order) as a unit? 5040 (c) How many ways can the letters of the word ANCESTOR be arranged in a row if the letters CES must remain together (in order) as a unit? 720 (Hint: See Exercise 9.2.39 with its solution in the "Read It" link.)

(a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with 8 elements. So the answer is 40,320 (b) How many ways can the letters of the word ANCESTOR be arranged in a row if A and N must remain together (in order) as a unit? 5040 (c) How many ways can the letters of the word ANCESTOR be arranged in a row if the letters CES must remain together (in order) as a unit? 720 (Hint: See Exercise 9.2.39 with its solution in the "Read It" link.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
Is my answer correct?
(a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with 8 elements. So the answer is 40,320 (b) How many ways can the letters of the word ANCESTOR be arranged in a row if A and N must remain together (in order) as a unit? 5040 (c) How many ways can the letters of the word ANCESTOR be arranged in a row if the letters CES must remain together (in order) as a unit? 720 (Hint: See Exercise 9.2.39 with its solution in the "Read It" link.)
Transcribed Image Text:(a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with 8 elements. So the answer is 40,320 (b) How many ways can the letters of the word ANCESTOR be arranged in a row if A and N must remain together (in order) as a unit? 5040 (c) How many ways can the letters of the word ANCESTOR be arranged in a row if the letters CES must remain together (in order) as a unit? 720 (Hint: See Exercise 9.2.39 with its solution in the "Read It" link.)
Detinition An rpermutauon of a set of n eleinentx i as orleced selectioN of relensents taken fmin the set of n elements, The nunber of teecetations of a Det sf si leamate in denurd P(,r). Theorem 9.2.3 it and are atege and1ceSK then the niember of esernstations of a set ofelenienta is Sivea by the fornula Firit rendos 01; equivalently, coad verdoa. a How many ways can three of the letters of the word ALGORITHM be selected and written in a row? 39 MAT 250 – Introduction to Discrete Structures Dr. Feuer b. How many ways can six of the letters of the word ALGORITHM be selected and written in a row? a Pe=(60,480/ c How many ways can six of the letters of the word ALGORITIM be selected and written in a row if the first letter must be A? T =6,720 VEST d. flow many ways can six of the Intters of the word ALGORITHM be nolected and writien in a row if the first two letters must be OR?
Transcribed Image Text:Detinition An rpermutauon of a set of n eleinentx i as orleced selectioN of relensents taken fmin the set of n elements, The nunber of teecetations of a Det sf si leamate in denurd P(,r). Theorem 9.2.3 it and are atege and1ceSK then the niember of esernstations of a set ofelenienta is Sivea by the fornula Firit rendos 01; equivalently, coad verdoa. a How many ways can three of the letters of the word ALGORITHM be selected and written in a row? 39 MAT 250 – Introduction to Discrete Structures Dr. Feuer b. How many ways can six of the letters of the word ALGORITHM be selected and written in a row? a Pe=(60,480/ c How many ways can six of the letters of the word ALGORITIM be selected and written in a row if the first letter must be A? T =6,720 VEST d. flow many ways can six of the Intters of the word ALGORITHM be nolected and writien in a row if the first two letters must be OR?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS