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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:

  1. $2$
  2. $3$
  3. $4$
  4. $5$
in Numerical Ability 4.9k points
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1 Answer

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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 $(B).$

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