GATE Civil Engineering
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Four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{R}$ cannot sit adjacent to each other. $\text{S}$ should be seated to the right of $\text{Q}$. The number of distinct seating arrangements possible is:

  1. $2$
  2. $4$
  3. $6$
  4. $8$
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Given that, four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row.

  • $\text{P}$ and $\text{R}$ cannot sit adjacent to each other.
  • $\text{S}$ should be seated to the right of $\text{Q}$. 

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

  • $\begin{array}{|c|c|c|}\hline  {\color{Red}{Q}} & P & {\color{Blue}{S}} & R \\\hline\end{array}$
  • $\begin{array}{|c|c|c|}\hline  {\color{Red}{Q}} & R & {\color{Blue}{S}} & P \\\hline\end{array}$
  • $\begin{array}{|c|c|c|}\hline  P & {\color{Red}{Q}} & {\color{Blue}{S}} & R \\\hline\end{array}$
  • $\begin{array}{|c|c|c|}\hline  R & {\color{Red}{Q}} & {\color{Blue}{S}} & P \\\hline\end{array}$
  • $\begin{array}{|c|c|c|}\hline P & {\color{Red}{Q}} & R & {\color{Blue}{S}}  \\\hline\end{array}$
  • $\begin{array}{|c|c|c|}\hline R & {\color{Red}{Q}} & P & {\color{Blue}{S}}  \\\hline\end{array}$

$\therefore$ The number of distinct seating arrangements possible $ = 6.$

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

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