Question: number of triangles that can be formed from n points?
Answer: The number of triangles is 1, 8, 35, 110, 287, 632, 1302, 2400, 4257, 6956 for polygons with 3 through 12 sides. If we connect all vertices of a regular N-sided polygon we obtain a figure with = N (N - 1) / 2 lines. For N=8, the figure is: Careful counting shows that there are 632 triangles in this eight sided figure.