This question is equivalent to placing $2000$ objects in (10000 - 2000) boxes with exactly one empty box. But, it is in circular fashion. We'll take care of it afterwards.

So, $x_1 + x_2 + ...... + x_{2000} = 8000$

Let $x_1 \geq 0 \text{ and } x_2, x_3 .... x_{2000} \geq 1$

$\text{No. of ways of distribution } = {8000 \choose 1999}$

Now, there are $2000$ ways of selecting $x_i \geq 0$

$\text{ways } = 2000 × {8000 \choose 1999}$

To take care of circular fashion, we have to multiply it by $10000$ and divide it by $2000$

$\color{#3D99F6}{\boxed{\text{total ways } = 10000 × {8000 \choose 1999}}}$

$a = 10000, b = 8000 \text{ and } c = 1999$

$\boxed{a + b + c = 19999}$