Triangles are formed with vertices of a regular polygon of 20 sides. The probability that no side of the polygon is a side of the triangle is $\frac{λ}{57}$ Then $\frac{λ}{40}$ is___

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Solution

The total number of triangles that can be formed is 20C3 = 1140. There are 20 triangles with two sides of polygon. There are $20 \times 16$ triangles with one side of polygon
$∴$ required probability $= \frac{1140 - 20 - 320}{1140} = \frac{800}{1140} = \frac{40}{57}$
=> Answer = 40/40
= 1

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Triangles are formed with vertices of a regular polygon of 20 sides. The probability that no side of the polygon is a side of the triangle is λ57 Then λ40 is___

The total number of triangles that can be formed is 20C3 = 1140. There are 20 triangles with two sides of polygon. There are 20×16 triangles with one side of polygon ∴ required probability =1140−20−3201140=8001140=4057 => Answer = 40/40 = 1

Triangles are formed with vertices of a regular polygon of 20 sides. The probability that no side of the polygon is a side of the triangle is $\frac{λ}{57}$ Then $\frac{λ}{40}$ is___

The total number of triangles that can be formed is 20C3 = 1140. There are 20 triangles with two sides of polygon. There are $20 \times 16$ triangles with one side of polygon
$∴$ required probability $= \frac{1140 - 20 - 320}{1140} = \frac{800}{1140} = \frac{40}{57}$
=> Answer = 40/40
= 1