We admit that Vandermonde's identity remains valid for all natural integers $u, v, N$: $$\binom{u+v}{N} = \sum_{k=0}^{N} \binom{u}{k} \binom{v}{N-k}.$$ Give a combinatorial interpretation of Vandermonde's identity.
We admit that Vandermonde's identity remains valid for all natural integers $u, v, N$:
$$\binom{u+v}{N} = \sum_{k=0}^{N} \binom{u}{k} \binom{v}{N-k}.$$
Give a combinatorial interpretation of Vandermonde's identity.