Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
Of 5 employees, 3 are to be assigned an office and are to be assigned a cubicle. If 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?
(A) 1/3
(B) 2/5
(C) 1/2
(D) 3/5
(E) 2/3
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 
.