Total number of triangle possible: [math]\binom{6}{3}=20[/math] all equiprobable.[br]Number of right triangle: each vertex has 2 triangles with right angle at the vertex. Thus a total of 6x2=12 right triangles.[br]Answer is 12/20.

Three distinct vertices of a regular hexagon are chosen at random and a triangle is formed by joining the three vertices. What is the probability that the triangle formed is a right triangle? Express your answer as a common fraction.