Question

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 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 that these 4 offices assigned to 4 employees $=4!$<div>&#160;$i.e=4\times 3\times 2\times 1\times =24$

If $Karen$ is at leftmost and $Tina$ is at rightmost, number of ways that can be filled with other employees $=2\times 1=2$

Similarly, If $Karen$ is at rightmost and $Tina$ is at lefttmost, number of ways that can be filled with other employees $=2\times 1=2$

$P\left(A\right)=\frac{Numberoffavorableoutcomes}{TotalNumberofpossibleoutcomes}$

Probability $P\left(A\right)=\frac{2+2}{24}=\frac{1}{6}$

hence, option $C$ is correct.