10. Given the set $M=\{1,2, \cdots, 99\}$. Now, nine elements are randomly selected from $M$ to form a subset, and the smallest number in this subset is denoted as $\xi$. Then $\mathrm{E} \xi=$ $\qquad$.
10. 10 .

For a set $M$, the number of nine-element subsets with the smallest number being a positive integer $k (1 \leqslant k \leqslant 99)$ is $\mathrm{C}_{99-k}^{8}$.
$$
\begin{array}{l}
\text { Hence } P(\xi=k)=\frac{\mathrm{C}_{99-k}^{8}}{\mathrm{C}_{99}^{9}} \\
\Rightarrow \mathrm{E} \xi=\sum_{k=1}^{91} \frac{k \mathrm{C}_{99-k}^{8}}{\mathrm{C}_{99}^{9}}=\frac{1}{\mathrm{C}_{99}^{9}} \sum_{k=8}^{98} \sum_{j=8}^{k} \mathrm{C}_{j}^{8} \\
\quad=\frac{1}{\mathrm{C}_{99}^{9}} \sum_{k=8}^{98} \mathrm{C}_{k+1}^{9}=\frac{\mathrm{C}_{100}^{10}}{\mathrm{C}_{99}^{9}}=10 .
\end{array}
$$