CA Foundation · Quantitative Aptitude · Permutations and Combinations
In how many ways can 6 persons be seated around a circular table if two particular persons, Anil and Bina, must NOT sit next to each other?
The answer is 72. Total circular seatings of 6 persons are 5! = 120. With Anil and Bina together, there are 4! × 2 = 48 seatings. Subtracting gives 120 - 48 = 72. The figure 48 counts the together cases, not the required ones.
- A120
- B48
- C72Correct
- D24
Explanation
Total circular arrangements = (6-1)! = 120. Arrangements with Anil and Bina together: treat as one unit, giving (5-1)! × 2 = 24 × 2 = 48. Not together = 120 - 48 = 72. Option 48 is the number of arrangements where they ARE together.
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