What is the probability that the married couple will have nonadjacent desks? Problem in Description.

Question

Seven new employees, two of whom are married to each other, are to be assigned seven 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

Well the desks can be assigned in 7! ways = 5040 ways

Suppose employees A,B are married to each other

and suppose their desks are adjacent

then if the desks are numbered 1.. 7 we can have

1 2 3 4 5 6 7

A B

B A

A B

B A

A B

B A

A B

B A

A B

B A

A B

B A

so 12 ways

So number of ways when desks nonadjacent = 5040 - 12 = 5028

So probability = 5028 / 5040 = 0.998