CA Foundation · Quantitative Aptitude · Seating Arrangements
In how many ways can 6 persons be seated in a row such that two particular persons, A and B, do not sit next to each other?
The answer is 480. Without any restriction, 6 persons can sit in 720 ways. Arrangements with A and B together number 5! × 2 = 240. Subtracting these from the total gives 720 − 240 = 480 arrangements where they are not adjacent.
- A240
- B360
- C480Correct
- D600
Explanation
Total arrangements of 6 persons in a row are 6! = 720. Treating A and B as one block gives 5! = 120 arrangements, and A and B can be ordered inside the block in 2 ways, so 240 arrangements have them together. The required number is 720 − 240 = 480. The option 600 comes from forgetting the 2 ways of ordering A and B inside the block (720 − 120).
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