Thread: problem in combinatorics

a regular polygon has n sides.how many triangles can be drawn using the vertices,but not the sides?
i thought that the solution is 20C3 but it is not.could you please explain.

20C3 is the total number of triangles, including those that use the polygon's sides. You need to subtract such triangles. For this it is convenient to count separately the number of triangles that use exactly one or exactly two of polygon's sides.