(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
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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

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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.

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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]

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