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_43e7ff204cbd87ef9854g-13.jpg?height=60&width=2001&top_left_y=1554&top_left_x=17)

## Answer

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