If 15 people sit around a round table then the unfavourable chance ratio of two particular persons sitting together is

$$\begin{gathered} \mathrm{Number} \mathrm{of} \mathrm{ways} \mathrm{in} \mathrm{which} 15 \mathrm{people} \mathrm{sit} \mathrm{around} \mathrm{a} \mathrm{round} \mathrm{table} \mathrm{is} 14!. \\ \mathrm{Two} \mathrm{persons} \mathrm{sit} \mathrm{together} \mathrm{consider} \mathrm{them} \mathrm{as} \mathrm{one} \mathrm{unit} \\ \therefore \mathrm{no} \mathrm{of} \mathrm{persons} \mathrm{to} \mathrm{be} \mathrm{arranged} =15-2+1=14 \\ \Rightarrow \mathrm{No} \mathrm{of} \mathrm{circular} \mathrm{permutations}=(14-1)!2!=13! 2! \\ \text{ Ratio }=\left(1-\frac{2.13!}{14!}\right):\frac{2.13!}{14!}=\frac{6}{7}:\frac{1}{7} \end{gathered}$$