Question

The figure 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 with an X?

• A. $\frac{1}{16}$
• B. $\frac{1}{12}$
• C. $\frac{1}{6}$
• D. $\frac{1}{4}$
• E. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{1}{6}$

Total number of ways these four offices could be assigned to four people $=4\times 3\times 2\times 1=24$

If Karen is in the left most and Tina is in the right most the rest of the positions could be filled by $2\times 1$.

If Tina is in the leftmost and Karen in the right most, again you have two ways to fill the four offices. The total number is $4$.

Thus the probability is:

$\frac{4}{24}=\frac{1}{6}$.