8. If positive integers $a, b, c$ satisfy $2017 \geqslant 10 a \geqslant 100 b \geqslant 1000 c$, then the number of tuples $(a, b, c)$ is
$\qquad$ .
Given that $1 \leqslant c \leqslant 2$, when $c=2 \Rightarrow b=20 \Rightarrow a=200,201$, at this point the array $(a, b, c)$ has 2 instances;
When $c=1$, $10 \leqslant b \leqslant 20, 10b \leqslant a \leqslant 201$.
If $b=10 \Rightarrow 100 \leqslant a \leqslant 201$, at this point the array $(a, b, c)$ has 102 instances;
If $b=11 \Rightarrow 110 \leqslant a \leqslant 201$, at this point the array $(a, b, c)$ has 92 instances;
If $b=12 \Rightarrow 120 \leqslant a \leqslant 201$, at this point the array $(a, b, c)$ has 82 instances;
If $b=20 \Rightarrow 200 \leqslant a \leqslant 201$, at this point the array $(a, b, c)$ has 2 instances.
Therefore, the array $(a, b, c)$ has a total of $\frac{11 \times(2+102)}{2}+2=574$ instances.