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in Olympiad by (75.8k points)

Suppose 40 objects are placed among a circle at equal distance. In how many ways can 3 objects be chosen from among them so that no two of the three objects are adjacent nor diametrically opposite ?

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x + y + z = 37

x ≥ 1, y ≥ 1, z ≥ 1

=> x = x’ + 1, y = y’ + 1, z = z’ + 1

x’ + y’ + z’ = 34

No of solution of ways

(let a1, a2, a3 ……………….. a40 are then if x = 19 then the objects selected becomes diametrically opposite.

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