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Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is

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a
12
b
15
c
110
d
120

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detailed solution

Correct option is C

Out of 6 vertices, 3 can be chosen  6C3, ways. The triangle will be equilateral if it is ΔACE or ΔBDF (2 ways). Therefore, the required probability is2 6C3=220=110


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