Problem 648

[Solution] For positive integers $k, 3 \leqslant k \leqslant 10$, every selection of $k$ points can form a convex polygon, and different sets of points form different polygons. There are $C_{10}^{k}$ different ways to choose $k$ points. Since
$$\begin{aligned} & C_{10}^{3}+C_{10}^{4}+C_{10}^{5}+\cdots+C_{10}^{10} \\ = & 2^{10}-C_{10}^{0}-C_{10}^{1}-C_{10}^{2}=968, \end{aligned}$$

a total of 968 different convex polygons can be formed.