8. If positive integers $a, b, c$ satisfy
$$
2019 \geqslant 10 a \geqslant 100 b \geqslant 1000 c \text {, }
$$

then the number of arrays $(a, b, c)$ is $\qquad$ .
8. 574.

Let $[x]$ denote the greatest integer not exceeding the real number $x$.
From the condition, we know that $c \leqslant\left[\frac{2019}{1000}\right]=2$.
When $c=1$, $10 \leqslant b \leqslant 20$, for each such positive integer $b$, by $10 b \leqslant a \leqslant 201$, the number of corresponding $a$ is $202-10 b$. Therefore, the number of such positive integer triples is
$$
\sum_{b=10}^{20}(202-10 b)=\frac{(102+2) \times 11}{2}=572 .
$$

When $c=2$, we have
$$
\begin{array}{l}
20 \leqslant b \leqslant\left[\frac{2019}{100}\right] \Rightarrow b=20 \\
\Rightarrow 200 \leqslant a \leqslant\left[\frac{2019}{10}\right]=201 \\
\Rightarrow a=200,201 .
\end{array}
$$

In this case, there are two sets of $(a, b, c)$.
In summary, the number of positive integer triples that satisfy the condition is
$$
572+2=574 .
$$