   Chapter 9.3, Problem 13ES ### 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 group of eight people are attending the movies together.(a) Two of the eight insist on sitting side-by-side. In how many ways can the eight be seated together in a row? (b)Two of the people do not like each other and do not want to sit side-by-side. Now how many ways can the eight be seated together in a row?

To determine

(a)

To find the number of ways so that eight be seated together in a row.

Explanation

Given information:

A group of eight people

Concept used:

P(n,r)=n!nr!

Calculation:

The objective is to find the number of ways that eight people are seated beside each other.

If two people are sitting side by side, then there are 7 possible ways of selecting adjacent places.

Consider the two people as one person, and then the number of arrangements for 7 sitting is P(7,7) ways.

As the two people can be arranged in P(2,2) ways then the total number of arrangements is:

P

To determine

(b)

To find how many ways can the eight be seated together in a row.

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