9,10
$[\underline{\text { Equations in integers }}]$
How many solutions does the equation $x_{1}+x_{2}+x_{3}=1000$ have
a) in natural numbers b) in non-negative integers?
![](https://cdn.mathpix.com/cropped/2024_05_06_16504755117b31808ad7g-24.jpg?height=60&width=2020&top_left_y=2451&top_left_x=-1)

## Answer

a) $C_{999}^{2}$;
b) $C_{1002}^{2}$ solutions.