Equilateral triangles with $3$ vertex in a regular hexagon

Question

The problem is: What is the probability of making an inscribed equilateral triangle, taking $3$ vertex of a regular hexagon?.

I think the answer is $1/10$ but i don't know how to do it with combinatorics.

Answer 1

HINT

In a regular hexagon $ABCDEF$, you pick 3 vertices (order is not important). If you pick $ACE$ or $BDF$, you end up with equilateral triangle you desire.

• How many total vertex selections are possible?
• What is the probability of getting the desired result?