Question

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

• A. $\frac{24!}{13\times 11!}$
• B. $\frac{24!}{11\times 13!}$
• C. $13!$
• D. None of these

Answer 1

The correct option is A $\frac{24!}{13\times 11!}$

In this case of circular table the clockwise and anticlockwise orders are different,
then the required number of circular permutations = ${}^{24}{C}_{13}\times 12!=\frac{24!}{13\times 11!}$