2. Mark 10 points on a circle, how many different polygons can be formed using these points (all or part)? (Polygons are considered the same only if their vertices are exactly the same).


$$
\begin{array}{l}
\left.+C_{10}^{2}+\cdots+C_{10}^{0}+C_{10}^{10}\right]-\left[C_{10}^{0}+C_{10}^{\overrightarrow{1}}\right. \\
\left.+C_{10}^{2}\right]=(1+1)^{10}-(1+10+45)=968 \text{ different convex polygons.} \\
\end{array}
$$

For $3 \leqslant k \leqslant 10$, every selection of $k$ points can form a convex $k$-gon, i.e., $k$ points can be chosen in $C_{10}^{\mathrm{E}}$ ways,