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: first find the probability that the couple will have adjacent desks, and then subtract this number from 1.)

Here I'm using the hint, so I'm computing the probability that the two employees have adjacent desks. First of all we compute how many configurations are possible. Since there are 6 employees, the possible permutations (assignments to desks) are 6 factorial, i. e. 6 x 5 x 4 x 3 x 2 x 1 = 720. The couple could be in positions (1,2), (2,3), (3,4), (4,5), (5,6), and in every of these cases they can be in either order (so 5 x 2 cases) and in each of these cases the other 4 employees can be in any order (so 5 x 2 x 4! = 5 x 2 x 4 x 3 x 2 x 1) = 240. So, in 240 cases out of 720 the married employees are sit aside. Hence the probability we are looking for is 1 - 240/720 = 480/720 = 2/3 = 0.6666 ... = 66.666 %.