Now, you must find the number of each type is possible. (do not over-count)
The area a regular hexagon is where is the length of a side in the hexagon.
Next, you need to find the area of each type of triangle.
You are looking for the ratio of the area of the triangles to area of the hexagon.
If you know complex variables the set of numbers form a hexagon inscribed in the unit circle. From that you can use the semi-perimeter rule to find the area of each of the three types of triangles.
If you don't know complex variables, I don't know how to help you further.