Consider 6 vertices of a regular hexagon and its centre. Triangles are formed by joining any three points out of seven points and if pq(where p and q are co-prime number) denotes the probability that the triangle is equilateral then the value of (p + q) is

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Consider 6 vertices of a regular hexagon and its centre. Triangles are formed by joining any three points out of seven points and if $\frac{p}{q}$ (where p and q are co-prime number) denotes the probability that the triangle is equilateral then the value of (p + q) is

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Detailed Solution

Total number of triangles $^{7} C_{3} - 3 = 35 - 3 = 32$

Number of equilateral triangle if $Z_{0}$ is not used = 2

Number of equilateral triangle if $Z_{0}$ is used =6

Total number of equilateral triangle = 8

Required probability

p + q = 5

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