The correct answer is D

Explanation

Of the??office workers,??are to be assigned an office. This is an example of combinations: to find the number of ways of choosing??of the??workers, you can count the number of ways of selecting the workers one at a time and then divide by the number of times each group of??workers will be repeated.

There are??ways of choosing the first worker to get an office. Then there will be?ways of choosing the second worker to get an office, and??ways of choosing the third worker. This is a total of??possibilities. In these??possible selections, each distinct group of??workers will occur??times. (There are?possibilities for the first worker chosen from the group,??for the second worker chosen, and only??for the third.) Therefore, there are??different ways the?workers who get an office can be chosen from the??workers.

How many of these??possible groups of??workers consist of??men and?woman? From the??male workers,??can be chosen in??different ways. There are?possibilities for the female worker. Therefore,??of the groups of??workers consist of??men and??woman.

Since there are??different ways the??workers who get an office can be chosen, and?of these possible groups of??workers consist of??men and??woman, the probability that the offices will be assigned to??men and??woman is?, or?.