$n > k > 0$. $n,k \in \mathbb{N}$
Prove combinatorially (without algebric manipulation): $\sum_{r=0}^n (-1)^r \binom{n}{r}CC^{k-r}_n = 0$
Note: $CC^{k}_n$ is the number of options to choose $k$ objects out of $n$ different types with repetitions and without order. For example it is the same as the number of options to put $k$ balls in $n$ cells (no order for cells, with repetitions of balls in each cell). It is equal to $\binom{n+k-1}{k}$
I have no clue sadly, looking for a hint on how to approach this.