Question

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?

Answer 1

Six employees can be arranged in 6! ways. n( *) = 6!

Two adjacent desks for married couple can be selected in 5 ways viz.,(l, 2), (2, 3), (3,4), (4, 5), (5,6).

This couple can be arranged in the two desks in 2! ways. Other four persons can be arranged in 4! ways.

So, number of ways in which married couple occupy adjacent desks = 5×2! x4! =2×5!

So, number of ways in which married couple occupy non-adjacent desks = 6! – 2 x 5! = 4 x 5! = n(E)