Nine new employees, two of whom are married to each other, are to be assigned nine...

Nine new employees, two of whom are married to each other, are to be assigned nine 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 nonadjacent desks is the complement of the event that they have adjacent desks.) (Round your answer to the nearest tenth of a percent.)

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Expert Solution

Of 9 new employees, 2 employees are married to each other; these 9 employees are to be assigned 9 desks that are lined up in a row.

If the assignment of the employees to the desks is made randomly, we have to find the probability that the married couple will have non adjacent desks.

Now, the event that the couple have non adjacent desks is the complement of the event that they have adjacent desks.

Now, first let us determine in how many ways can the couple have adjacent desks.

Let us consider the married couple as a single entity, that always stays together.

Then, in total, there are 8 entities; 7 non related employees and 1 married couple.

Now, these 8 can be arranged among themselves in 8! number of ways.

The married couple can have adjacent desks in 2! ways.

So, the favourable number of cases, in which the couple has adjacent desks, is 8!*2!.

Again, 9 employees can be assigned desks in 9! number of possible ways.

That is, the number of all possible cases is 9!.

This means that

P(The couple has adjacent desks)

=8!*2!/9!

=0.2222.

Now,

P(The couple will have non-adjacent desks)

=1-P(The couple will have adjacent desks)

=1-0.2222

=0.7778

The answer is

The married couple will have non-adjacent seats with probability approximately 0.7778.

orchestra answered 1 year ago

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