   Chapter 9.3, Problem 21ES ### 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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# Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks? (Hint: The event that the couple have non-adjacent desks is the complement of the event that they have adjacent desks.)

To determine

Six new employees. two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, wflat is the probability that the married couple will have nonadjacent desks? (Hint: First find the probability that the couple will have adjacent desks, and then subtract this number from 1 .)

Explanation

Given information:

We can consider the couple as one employ, then there are effectively 5 desks to assign.

Concept used:

Probability of not occurring the event E is given by

P(E)=1P(E)

Calculation:

Again the couple can interchange their desks to each other in 2 ways.

By multiplication rule, the number of ways to assign 5 desks to 5 employees is 5!

By multiplication rule. the number of ways to assign desks such that couple has adjacent desks is 2(5!)

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