Question

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these vertices is equilateral, is
(a) $\frac{3}{10}$

(b) $\frac{3}{20}$

(c) $\frac{1}{20}$

(d) $\frac{1}{10}$

Answer 1

Total number of triangles which can be formed is equal to ⁶C₃ = $\frac{6\times 5\times 4}{1\times 2\times 3}=20$ and hexagon has 2 equilateral triangles.
∴ Probability that the triangle with these vertices is equilateral is = $\frac{2}{20}=\frac{1}{10}$
Hence, the correct answer is option D.