8. Teacher Li is buying souvenirs for students. The store has bookmarks, postcards, notebooks, and pens, four types of souvenirs, each with 10 items (all items of the same type are identical). Teacher Li plans to buy 25 souvenirs, and at least one item of each type must be purchased. Then there are $\qquad$ different purchasing schemes (answer with a number).
8.592.

Just calculate the coefficient of $x^{25}$ in $f(x)=\left(x+x^{2}+\cdots+x^{10}\right)^{4}$.
Notice that,
$$
\begin{array}{l}
f(x)=\left(\sum_{i=1}^{10} x^{i}\right)^{4}=x^{4} \cdot \frac{\left(1-x^{10}\right)^{4}}{(1-x)^{4}} \\
=x^{4}\left(1-4 x^{10}+6 x^{20}-4 x^{30}+x^{40}\right) \sum_{n=0}^{\infty} \mathrm{C}_{n+3}^{3} x^{n} .
\end{array}
$$

Therefore, the coefficient of $x^{25}$ is $\mathrm{C}_{24}^{3}-4 \mathrm{C}_{14}^{3}+6 \mathrm{C}_{4}^{3}=592$.