In how many ways, can 24 persons be seated around a circular

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In how many ways, can 24 persons be seated around a circular table if there are is 13 seats?

1. 24! / [13 x 11! ]
2. 22! / [14 x 12!]
3. 23! / [13 x 11!]
4. 24! / [12 x 12!]
5. None of the above

Correct Option: A

First , we select 13 persons out of 24 persons in ²⁴C₁₃ ways.
Now, these 13 persons can be seated in 12! ways around a table .

So required number of ways = ²⁴C₁₃ x 12!
= [24! / {13!(24 - 13)!}] x 12!
= [24! / {13! x 11!}] x 12!
= 24! / (13 x 11!)