   Chapter 9.2, Problem 39ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# a. How many ways can three of the letters of the word ALGORITHM be selected and written in a row? b. How many ways can six of the letters of the word ALGORITHM be selected and written in a row? c. How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A? d. How many ways can six of the word ALGORITHM be selected and written in a row if the first two letters must be OR?

To determine

(a)

The number ways that three of the letters of the word ALGORITHM be selected and written in a row.

Explanation

Given information:

The objective is to find the number of ways to select three letters from ALGORITHM.

Concept used:

P(n,r)=n!nr!

Calculation:

The objective is to find the number of ways to select three letters from ALGORITHM.

When the letters are arranged randomly in a row, the total number of arrangements is:

9! = 362880.

The number or ways of selecting 3 letters from the word ALGORITHM is the number of 3 - permutations of a set of 9 elements

To determine

(b)

The number of ways that six letters of the word ALGORITHM be selected and written in a row.

To determine

(c)

The number of ways that six letters of the word ALGORITHM be selected and wrítten in a row if the first letter must be A.

To determine

(d)

How many ways can six of the letters of the world ALGORITHM be selected and written in a row if the first two letters must be OR ?

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