   Chapter 9.3, Problem 30ES ### 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 now in a classroom has n seats. Let s n be the number of ways nonempty sets of students can sit in the row so that no student is seated directly adjacent to any other student. (For instance, a row of three seats coulf contain a single student in any of the seats or a pair of contain a single student in any of the seats or a pair students in the two outer seats. Thu s 3 = 4 .) Find a recurrence relation for s 1 , s 2 , s 3 , ...

To determine

To find a recurrence relation for s1,s2,s3.

Explanation

Given information:

Now, sn be the number of ways nonempty sets of students can sit in the row so that no student is seated directly adjacent to any other student.

Calculation:

Let us consider a classroom of n seats.

Now, sn be the number of ways nonempty sets of students can sit in the row so that no student is seated directly adjacent to any other student.

Let us consider the case n=1.

In this case, only 1 student can be arranged in 1 way.

Thus, s1=1.

Let us consider the case n=2.

In this case, only 1 student can be arranged in 2 ways, either on first seat or on the second seat.

Thus, s2=2.

Let us consider the case n=3

In this case, either only 1 student can be arranged in 3 ways, or 2 students in 1 way.

Thus, s3=4

Let us consider the case n=4.

In this case, either only 1 student can be arranged in 4 ways, or 2 students in 3 ways

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