(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 elements. So the answer is (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? (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?

(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 elements. So the answer is (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? (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?

Name: **Exercise on Permutations: Arranging the Word "ANCESTOR"**Use the me
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: **Exercise on Permutations: Arranging the Word "ANCESTOR"**Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions.**(a)** How many ways can the letters of the word **ANCESTOR** be arranged in a row?- Since t

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Suppose an elementary school teacher wants to line up the students at the classroom door for…

Q: A class has 26 students. In how many different ways can five students form a group for an…

Q: Kelly has different books to arrange on a shelf, 4 blue, 3 green, and 2 red. Answer parts a through…

A: Answer of (a) is 4*3*2 = 24

Q: In how many ways can 4 different IT books, 2 different mathematics books, and 1 biology book be…

A: The objective of this question is to find the number of ways the books can be arranged on a…

Q: a. A dinner club has 30 members. At a particular dinner, every club member gets to order exactly 3…

Q: Ty's wardrobe consists of: • 10 unique shirts • 4 unique pants • 8 unique matched pairs of socks and…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: For some particular website, the password must start with one of the letters W, X, Y, or Z. Then…

A: We have 10 digits and 26 alphabets in totalFor first letter we have 4 possible choices (W,X,Y, or…

Q: A basketball team has 12 players on it. In how many different ways could a 5-player starting lineup…

Q: In how many ways can 7 science books, 3 history books, and 6 mathematics books be arranged on a…

Q: how many ways can 5 textbooks, 3 coffee table books and 2 novels be arranged if the textbooks must…

A: This question is from permutation We have to calculate, in how many ways 5 textbooks, 3 coffee table…

Q: The Beatles had 27 number one hits; a radio station asks listeners to send in a list ranking their…

A: Solution: So, There are 27 number one hits of Beatles So a listener asked to rank top 7 ranges.

Q: A class has 35 students. In how many different ways can four students form a group for an activity?…

Q: In how many ways can 7 children and 6 mother be arranged in a row so that: No two children are sit…

Q: ways cal on a bookshelf if 6 different novels, 6 different mathematics books, and 2 blology DOOK(S)…

Q: Bob owns 13 different books. He wants to pick out and arrange 5 of these books left-to-right on a…

Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

A: Factorial Rule: The total number of ways n different objects can be arranged where the order of the…

Q: Five paintings in an art gallery have the following names: "red," "seascape," "flower," "horse," and…

A: Given: Total number of names = 5 Number of names chosen without repetition = 3

Q: 2) A school district assigns each of their students a password that consists of three unique letters…

A: Solution

Q: Six rock songs and five rap songs are on a disc jockey's playlist for a radio show. How many…

A: We need to find number of possible ways.

Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Topic Video

Question

**Exercise on Permutations: Arranging the Word "ANCESTOR"**

Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions.

**(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 [textbox] elements. So the answer is [textbox].

**(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?

- [textbox]

**(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?

- [textbox]

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Permutation and Combination$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

In how many ways can we paint the 10 rooms of a hotel if at most 3 can be painted red, at most 2 painted green, at most 1 painted white, and any number can be painted blue or orange? (The rooms are different, so order matters.)
For some particular website, the password must start with one of the letters W, X, Y, or Z. Then there must be 4 more charaters, and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible?
In a cars carrier, how many ways are there to put 5 cars labeled as {A, B,..., E} in 4 containers labeled as {1, 2, 3, 4}? Each container must include at least one car. Your answer is If the containe #1 must have the car A in it, find the new number of possible ways. Your answer is
A certain brand of shoes comes in 4 different styles, with each style available in 4 distinct colors. If the store wishes to display pairs of the shoes showing all of its various styles and colors, how many different pairs will the store have on display? They will have different pairs of shoes on display. (Type a whole number.)
Suppose we have 5 alphabets (a, b, c, d, e) and 5 envelops (?1,?2,?3,?4,?5) In how many ways we can place such that- A. At least one letter is wrongly placed B. At least one letter is correctly placed
How many different birth orders with respect to gender are possible in a family with six children (For example, BBBGGG & BGBGGB are different orders
3.) Find the number of distinguishable permutations of the letters in each word. (a) subsets (b) dreidel (c) depleted
In how many ways can 3 paper toys, 7 rubber toys, and 5 plastic toysbe arranged in a row if:(A)toys of the same material type must be grouped together;(B)rubber toys should not be next to each other?
A bookshelf contains ten books, of which some are indistinct. In fact, five of the books are identical calculus textbooks, while three of them are identical stats books. The other two books are identical trig books. How many distinguishable arrangements of these ten books is possible?