Question

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?

Answer 1

³⁶C₃ – 36 – 36 (32) — 18 × 30

Total ways of 3 selections = ³⁶C₃

Three at adjacent positions = 36

Exactly two at consecutive positions = 36 × 32

Diametrically opposite but not adjacent = 36 x 30/2

So ³⁶C₃ – 36 – 36 × 32 – 18 × 30

= 5412