Consider a circle of any radius. If $n \geq 3$ points are chosen on the circumference of the circle, how many triangles can drawn such that each vertex of the triangle on the points that have been chosen? Assume that if three distinct points do not lie in the same straight line then they are in a triangle.
My thought is $^n C _3$ is the number of such triangles, but I am not sure. Can someone offer me a better answer.