Project ForgeFive persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. 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. The number of distinct seating arrangements possible is:
- A2
- 3
- C4
- D5
Explanation
R is fixed at position 2. Since P and T cannot be at either end (positions 1 or 5), and position 2 is taken by R, both P and T must occupy positions 3 and 4 (2 orderings). The remaining positions 1 and 5 go to Q and S (2 orderings), giving 4 total placements. Checking the 'P not adjacent to S' rule against each: only the placement with P=4,S=5 violates it (they'd be adjacent), leaving exactly 3 valid arrangements.
Source: GATE ME 2021 Session 2 (ME-2) (2021)
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