8. Arrange the numbers $1,2, \cdots, 6$ in any order. If the number $k$ appears exactly in the $k$-th position, it is called a match. The expected number of matches is $\qquad$
8. 1.

Let the matching number of digit $i$ be $\xi_{i}(i=1,2, \cdots, 6)$. Then $P\left(\xi_{i}=0\right)=\frac{\mathrm{C}_{5}^{1} \mathrm{~A}_{5}^{5}}{\mathrm{~A}_{6}^{6}}=\frac{5}{6}$, $P\left(\xi_{i}=1\right)=\frac{\mathrm{A}_{5}^{5}}{\mathrm{~A}_{6}^{6}}=\frac{1}{6}$.
Thus, $\mathrm{E} \xi_{i}=0 \times \frac{5}{6}+1 \times \frac{1}{6}=\frac{1}{6}$.
And the matching number of the permutation $\xi=\sum_{i=1}^{6} \xi_{i}$, so $\mathrm{E} \xi=\mathrm{E} \sum_{i=1}^{6} \xi_{i}=\sum_{i=1}^{6} \mathrm{E} \xi_{i}=6 \times \frac{1}{6}=1$.