CA Foundation · Quantitative Aptitude · Permutations and Combinations
Nine persons, including the two brothers Karan and Arjun, are to be seated around a circular table. In how many ways can they be seated so that Karan and Arjun are NOT next to each other?
The answer is 30240. Total seatings of nine people around a circle are 8! = 40320. With the two brothers together there are 7! × 2 = 10080 seatings. Subtracting gives 40320 - 10080 = 30240 arrangements in which they are not adjacent.
- A30240Correct
- B5040
- C35280
- D40320
Explanation
Total circular arrangements = 8! = 40320. Arrangements with the brothers together: treat them as one unit, giving 8 units, so 7! × 2 = 10080. Not together = 40320 - 10080 = 30240. The option 35280 subtracts only 5040, forgetting the factor 2.
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