GATE ME 2021 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
Five persons and are sitting in a row not necessarily in the same order. and are separated by one person, and should not be seated adjacent to . The number of distinct seating arrangements possible is:
Correct answer
(D) 16
Solution
Let the five positions in the row be 1, 2, 3, 4, and 5. The condition " and are separated by one person" means the possible pairs of positions for or are and .We also have the constraint that cannot be adjacent to .Let's analyze each case:
1.: cannot be at position 2. Thus, can be at 4 or 5. For each choice of , the remaining two persons ( and ) can be arranged in ways.
Total arrangements = .2.: cannot be at 1 or 3. Thus, must be at 5. The remaining two persons ( and ) can be arranged in ways.
Total arrangements = .3.: cannot be at 2 or 4. Thus, must be at 1. The remaining two persons ( and ) can be arranged in ways.
Total arrangements = .4.: cannot be at 2 or 4. Thus, must be at 5. The remaining two persons ( and ) can be arranged in ways.
Total arrangements = .5.: cannot be at 3 or 5. Thus, must be at 1. The remaining two persons ( and ) can be arranged in ways.
Total arrangements = .6.: cannot be at 4. Thus, can be at 1 or 2. For each choice of , the remaining two persons ( and ) can be arranged in ways.
Total arrangements = .Summing all cases: .Therefore, there are 16 distinct seating arrangements possible.Continue learning with Success Tracker
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