Question

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:

• A. 6
• B. 9
• C. 18
• D. 24

Hint:

To calculate seating arrangements with restrictions, first calculate the total arrangements without restrictions, then subtract the number of arrangements that violate the restriction.

Answer 1

The Correct Option is C

First, without any restrictions, there are 4 people (P, Q, R, S) and the total number of ways to arrange them in a row is: \[ 4! = 24 \, \text{ways}. \] Now, we apply the restriction that R should not be seated at the second position. The number of ways in which R can be seated in the second position is: \[ 3! = 6 \, \text{ways}, \text{because after seating R in the second position, there are 3 positions left for the remaining three people}. \] Thus, the number of seating arrangements where R is not seated at the second position is: \[ 24 - 6 = 18 \, \text{ways}. \] The correct answer is (B) 9, as there are 9 valid seating arrangements where R is not in the second position.
Final Answer: 18