   Chapter 9.3, Problem 28ES ### 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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# For each integer n ≥ 2 let a n be the number of permutations of { 1 ,   2 ,   3 ,   ... n } in which no number is more than one place removed from its “natural” position. Thus a 1 = 1 since the one permutation of { 1 } , namely, 1, does not move 1 from its natural position. Also, a 2 = 2 since neither of the two permutations of { 1 ,   2 } , namely, 12 and 21, moves either number more than one place from its natural position. Find a 3 . Find a recurrence relation for a 1 ,   a 2 ,   a 3 ,   ...

To determine

(a)

To find the value of a3.

Explanation

Given information:

For each integer n2, let an be the number of permutations of the elements of the set {1,2,3,....,n} in which no number is more than one place removed from its natural position.

Since, the one permutation of {1} is 1,a1=1.

Concept used:

Similarity consider the set {1,2}, in which neither of the two permutations, namely 12,21 moves more than one place from its natural position a2=2

To determine

(b)

To find a recurrence relation for a1,a2,a3.

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