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

Explanation

In case of circular table, the clockwise and anti-clockwise order are different, the required number of circular
permutations=`(.^(24)P_(13))/(13)=(24!)/(13xx11!)`
`impliesn!=nxx`number of circular arrangements of n different things
`implies`Number of circular arrangements of n different things
`=(n!)/(n)=(n-1)!`
Hence, the number of circular permutations of n different things taken all at a time is (n-1)!, if clockwise and anti-clockwise orders are taken as different.