In how many ways can $24$ persons be seated round a table, if there are $13$ seats ?

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$\frac{24!}{13 \times 11!}$

$\frac{20!}{10 \times 11!}$

$\frac{14!}{18 \times 11!}$

$\frac{15!}{10 \times 11!}$

answer is A.

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Detailed Solution

Total number of persons = 24

Total number of sets = 13

In case of circular table, the clockwise and anti-clockwise orders are different, the required number of circular permutations $= \frac{{}^{24}P_{13}}{13} = \frac{24!}{13 \times 11!} .$

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