In a party 23 persons take their seats at a round table. The odds against two particular persons sitting together are:

10 : 1

23 persons can sit at a round table in 22! ways.

The number of ways in which two particular persons sit together=21!× 2!

∴ Probability that two particular persons sit together $=\frac{21!× 2!}{22!}=\frac{1}{11}$

Hence, odd against two particular persons sit together are 10 : 1.          [∵ odd against =$P(\overline{A}): P(A)]$