The correct answer is D
Explanation
Of the 5 office workers, 3 are to be assigned an office. This is an example of combinations: to find the number of ways of choosing 3 of the 5 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 3 workers will be repeated.
There are 5 ways of choosing the first worker to get an office. Then there will be 4 ways of choosing the second worker to get an office, and 3 ways of choosing the third worker. This is a total of 5 times 4 times 3 = 60 possibilities. In these 60 possible selections, each distinct group of 3 workers will occur 3 times 2 times 1 = 6 times. (There are 3 possibilities for the first worker chosen from the group, 2 for the second worker chosen, and only 1 for the third.) Therefore, there are 60 over 6 = 10 different ways the 3 workers who get an office can be chosen from the 5 workers.
How many of these 10 possible groups of 3 workers consist of 2 men and 1 woman? From the 3 male workers, 2 can be chosen in 3 different ways. There are 2 possibilities for the female worker. Therefore, 3 times 2 = 6 of the groups of 3 workers consist of 2 men and 1 woman.
Since there are 10 different ways the 3 workers who get an office can be chosen, and 6 of these possible groups of 3 workers consist of 2 men and 1 woman, the probability that the offices will be assigned to 2 men and 1 woman is 6 over 10, or 3 over 5.
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