Six students sit in a row for an examination. If two of them, A and B, must not sit next to each other, the arrangement is easiest to count by
Correct answer: B. subtracting the arrangements where A and B are together from the total arrangements
- A. listing every possible order
- B. subtracting the arrangements where A and B are together from the total arrangements
- C. assuming A always sits first
- D. ignoring the restriction
Explanation
Counting the unwanted cases and subtracting them from the total is far quicker than enumerating what remains, and it is the standard complementary counting technique. Treating A and B as a single block gives the arrangements where they are together. The same approach handles most not adjacent conditions.
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About Seating Arrangements
Seating arrangement problems place people or objects in a line, circle, row or multiple rows according to positional clues. They require handling adjacency, left and right, facing directions, opposite seats, fixed positions and relative order, with circular arrangements differing because rotation does not create a new arrangement.
Practise Seating Arrangements
21 free Seating Arrangements MCQs from Analytical and Logical Reasoning, each with the correct answer and an explanation. Unlimited attempts, no account needed.
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