I have this excersice:
Determines the number of non-negative integer solutions of the equation: $rx_1 + x_2 + \cdots + x_n=kr$ where $k, r, n\in\mathbb{N}$.
I tried to use that the number of $r-combinations$ of the multiset $M=\{\infty\cdot a_1,\cdots,\infty\cdot a_k\}$ is equivalent to finding the number of non-negative integer solutions of the equation $x_1 + x_2 + \cdots + x_k=r$, so I was tempted to think that the answer to the excercise is $\sum_{x_1=0}^{k} \binom{r(k-x_1) + (n-1) - 1}{n-2 }$ but I'm not convinced by the fact that $x_1$ appears in the binomial coefficent, need help thinking about this.