Problem: Ten points are marked on a circle. How many distinct convex polygons of three or more sides can be drawn using some (or all) of the ten points as vertices? Solution: Any shape whose vertices occupy three or greater dots on the circle is convex, so this is a simple counting problem. The answer is $ \binom{10}{10}+\binom{10}{9}+\ldots+\binom{10}{3} = 2^{10}- \left(\binom{10}{2} + \binom{10}{1} + \binom{10}{0}\right) = 968 .$