1.83 Mark 10 points on a circle. How many different convex polygons can be constructed using some of these points as vertices? (Polygons are considered the same only if all their vertices coincide)


[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.