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GATE 2021 AE – Question 5

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

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. The number of distinct seating arrangements possible is:

  1. 6
  2. 9
  3. 18
  4. 24

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Correct answer: (C) 18

Explanation

**Total arrangements** of the four persons in a row: $4!=24$.

**Arrangements to exclude:** those with R at the second position from the left. Fix R there, and arrange P, Q, S in the other three positions: $3!=6$.

**Valid arrangements:**
$$24-6=\mathbf{18}.$$

(Direct count: R can be at any of the other 3 positions, and the remaining 3 people can be arranged in $3!=6$ ways, so $3\times6=18$.)