15 persons are sitting a round table. The number of ways of selecting three persons at a time from them, such that the selected three did not sit together at one place

Total no of ways of selecting 3 persons from 15 persons around a circular table = 15C₃.

No of ways of selecting 3 people who sit together = 15

Required no of ways  $=15{\mathrm{C}}_3-15$

$$\begin{gathered} =\frac{15\times 14\times 13}{3\times 2\times 1}-15=455-15 \\ =440 \end{gathered}$$