There are 12 persons sitting around a circular table. Then the number of ways of selecting 3 out of them such that no two persons are adjacent to each other

Total number of ways of selecting 3 out of 12 is  ${12}_{c_3}=220$
All these together (123, 234,….,(11, 12, 1)) $\to$ 12 ways
$\begin{array}{c}2togetherare1away\\ 12\mathrm{45....11}\left(8\right)\\ 23\mathrm{56....12}\left(8\right)\end{array}\}\to 12\times 8=96$