X _ _ X
The figure above represents four offices that will be assigned randomly to four employees, one employee per office. If Karen and Tina are two of the four employees, what is the probability that each will be assigned an office indicated an X?
I got 1/12 but the answer is 1/6. I don't understand how Karen and Tina have 4 possibilities for their positions.
Best Answer
There are $4! = 24$ possible assignments of employees to offices. We will suppose that the four employees are Karen, Tina, Alice and Bob.
The assignments of employees to offices where Karen and Tina get those offices are KABT, KBAT, TABK, and TBAK. There are four such assignments, so the probability that Karen and Tina are assigned those two offices is $\frac{4}{24} = \frac{1}{6}$.
(I think you might be forgetting that it doesn't matter which offices the other two employees are assigned to.)