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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?

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?

Answers (1)

Given: total number of employees = 6

They can be arranged in 6 ways:

Thus, n (S) = 6!

                = 6 x 5 x 4 x 3 x 1

                = 720

Now, there are 5 different ways to select two adjacent desks for married couples:

(1,2), (2,3), (3,4), (4,5), (5,6)

They can be arranged in two ways in the two desks, & the other persons can be arranged in four ways

Thus, the number of ways = 5 x 2! X 4!

                                    = 5 x 2 x 1 x 4 x 3 x 2 x 1

                                    = 240

Thus,

The number . of ways in which married couples occupy non-adjacent desks

= 6! – 240

= 720 – 240

= 480

= n (E)

 Required probability = number of favourable outcomes/total number of outcomes

= n (E) / n (S)   

= 480 / 720

= 2 / 3

Posted by

infoexpert22

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