Question

There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them, there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,$ $i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.

The probability that, on the examination day, the student $S_1$ gets the previously allotted seat $R_1$, and $NONE$ of the remaining students gets the seat previously allotted to him/her is

• A. $\frac{3}{40}$
• B. $\frac{1}{8}$
• C. $\frac{7}{40}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{3}{40}$

Number of ways, when only $S_1$ gets the previously allotted seat $R_1$
$=$ Dearrangement of other $4$ persons
$=4!(\frac{1}{0!}-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!})=9$
Total number of ways $=5!$
Required probability $=\frac{9}{5!}=\frac{3}{40}$