Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to
Answer & explanation
Correct answer: option 3
Total number of triangles which can be formed $= {^6C}_3 =\frac{6×5×4}{1×2×3}=20$
Number of equilateral triangles = 2.
∴ Required probability $=\frac{2}{20}=\frac{1}{10}.$