The odds against sitting of two particular persons together out of n persons seated round a circular table is :

$\mathrm{n}\left(\mathrm{S}\right)=(\mathrm{n}-1) !$

e=two particular persons sit together

$\begin{array}{rcl}\boxed{ \left| \right| }+\mathrm{n}-2& =& (\mathrm{n}-1) \mathrm{Units}\\ \mathrm{n}\left(\mathrm{E}\right)& =& (\mathrm{n}-2) ! 2!\\ \mathrm{P}\left(\mathrm{E}\right)& =& \frac{(\mathrm{n}-2) ! 2!}{(\mathrm{n}-1) !}=\frac{2!}{\mathrm{n}-1}\\ \mathrm{P}\left(\overline{\mathrm{E}}\right)& =& \frac{\mathrm{n}-3}{(\mathrm{n}-1)}\end{array}$

$\Rightarrow$ odd n against of event $\mathrm{E}=\mathrm{P}\left(\overline{\mathrm{E}}\right) : \mathrm{P}\left(\mathrm{E}\right)$

                                                   $=\mathrm{n}-3 : 2$