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12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is?

9 (10!)
2 (10!)
45 (8!)
10!

Correct Answer: 9 (10!)

Explanation:

12 persons can be seated around a round table in 11! ways. The total number of ways in which 2 particular persons sit side by side = 10! x 2!.
Hence, the required number of arrangements = 11! - 10! x 2! = 9 x (10!)

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