GATE Civil Engineering
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Four persons $P, Q, R$ and $S$ are to be seated in a row. $R$ should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

  1. $6$
  2. $9$
  3. $18$
  4. $24$
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It is given that, four persons $P, Q, R$, and $S$ are to be seated in a row. $R$ should not be seated at the second position from the left end of the row.

Now, we can make the possible arrangements.

  • From the left end, the second position can be filled in $3$ ways.
  • From the left end, the first position can be filled in $3$ ways.
  • From the right end, the second position can be filled in $2$ ways.
  • From the right end, the first position can be filled in $1$ way.

$$\boxed{\underset{1}{3}\quad \underset{2} 3 \quad\underset{3} 2 \quad \underset{4}1}$$

$\therefore$ The number of distinct seating arrangements possible $ = 3 \times  3 \times 2 \times 1 = 18.$

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

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