3 of the 6 vertices of a regular hexagon are chosen at random find the probability that the triangle with three vertices is equilateral.

Question

3 of the 6 vertices of a regular hexagon are chosen at random
find the probability that the triangle with three vertices is
equilateral

Ajanta Trivedi · Accepted Answer

out of 6 vertices, the number of ways to choose 3 vertices are ${}^{6}{C_{3}} = \frac{6!}{3! \cdot 3!} = \frac{6 * 5 * 4 * 3 * 2}{3 * 2 * 3 * 2} = 20$

the number of equilateral triangles that can be drawn from the vertices of a hexagon = 2 therefore the required probability = 2/2= = 1/10 hope this helps you