Question

Three of six vertices of a regular hexagon are chosen at random.The Probability that the triangle formed by these vertices is equilateral

• A. $\frac{1}{12}$
• B. $\frac{1}{5}$
• C. $\frac{1}{10}$
• D. None of these

Answer 1

The correct option is C $\frac{1}{10}$

Number of sides of regular hexagon $=6$. Any three sides can be chosen
in ${}^6{\text{C}}_3$ ways and there is only two set which formed
equilateral $△$ obtained by taking the vertices
alternatively.
Hence required probability $=\frac{2}{{}^6{\text{C}}_3}=\frac{2}{20}=\frac{1}{10}$