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Question

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

A
12
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B
15
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C
110
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D
120
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Solution

The correct option is D 110
n(S)= Number of ways of selection of 3 vertices out of 6 =6C3=20
Out of which there will be only two cases where triangle will be equilateral (By selecting ACE or BDF, where A,B,C,D,E,F are vertices of hexagon).
Hence required probability =220=110

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