1 vote

Five persons $\text{P, Q, R, S}$ and $\text{T}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{T}$ cannot be seated at either end of the row. $\text{P}$ should not be seated adjacent to $\text{S. R}$ is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

- $2$
- $3$
- $4$
- $5$

0 votes

Given that, five persons $P, Q, R, S$ and $T$ are to be seated in a row.

- $P$ and $T$ cannot be seated at either end of the row.
- $P$ should not be seated adjacent to $S.$
- $R$ is to be seated at the second position from the left end of the row.

Now, the five persons can be seated in the below arrangements:

- First we fix the position of $R,$ and now we have two choices for $P$ and $T,$ then place the $S$ and $Q$ in the remaining positions.
- $\begin{array}{|c|c|c|}\hline S & {\color{Red} {R}} & {\color{Green}{P}} & {\color{Blue}{T}} & Q \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline Q & {\color{Red} {R}} & {\color{Green}{P}} & {\color{Blue}{T}} & S \\\hline\end{array}$
- $\begin{array}{|c|c|c|}\hline S & {\color{Red} {R}} & {\color{Blue}{T}} & {\color{Green}{P}} & Q \\\hline\end{array}$

The number of distinct seating arrangements possible is $ = 3.$

So, the correct answer is $(B).$