Question

Triangles are formed by joining the vertices of a regular polygon of 20 sides. The probability that no side of the polygon is a side of the triangle, is

Answer 1

Given :- Triangles are formed by joining the vertices of a regular polygon of 20 sides. The probability that no side of the polygon is a side of the triangle, is ?

Answer :-

→ Total sides of polygon = 20

→ Total sides of a ∆ = 3 .

so,

→ Total numbers of ∆'s formed = 20(C)3 = 20!/(3! * 17!) = 20 * 19 * 18 / 3 * 2 = 1140 .

now,

→ ∆'s formed by using 1 side of polygon = 20 * 16 = 320

→ ∆'s formed by using 2 sides = 20

then,

→ Number of ∆'s formed with no sides of polygon = 1140 - (320 + 20) = 1140 - 340 = 800 .

therefore,

→ Required probability = 800/1140 = (40/57) (Ans.)

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