GATE CE 2021 Set 2 — Question 5
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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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:
Correct answer
(C) 18
Solution
Total number of persons = 4 (P, Q, R, S).
Total number of ways to arrange 4 persons in a row = .Now, let's find the number of arrangements where R is seated at the second position from the left end:
= .Therefore, the correct option is (C).
Total number of ways to arrange 4 persons in a row = .Now, let's find the number of arrangements where R is seated at the second position from the left end:
- Position 1: Can be filled by any of the remaining 3 persons (P, Q, S).
- Position 2: Fixed for R (1 way).
- Position 3: Can be filled by any of the remaining 2 persons.
- Position 4: Can be filled by the last remaining person.
= .Therefore, the correct option is (C).
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