# Selecting objects in a circle

Suppose 36 objects are placed along a circle at equal distances. In how many ways can 3 objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite?

Total ways of 3 selections = ${C_{3}}^{36}$
Three at adjacent positions = $36$
Exactly two at consecutive positions = $36 * 32$
Diametrically opposite but not adjacent = $\frac{36 * 30}{2}$
So ${C_{3}}^{36} – 36 – 36*32 – 18*30 = 5412$