# Proving Pascal's Triangle and Hockey-Stick Identity using Combinatorics [duplicate]

How would I prove the following using a combinatorial proof?

(a) Show that this identity is in Pascal's Triangle:
$$\sum_{k=0}^{n} \binom{n}{k}^{2} = \binom{2n}{n}, ∀n ∈ \mathbb{N}$$

(b) Prove the Hockey-Stick Identity: $$\sum_{k=0}^{m} \binom{n+k}{k} = \binom{n+m+1}{m}, ∀m, n ∈ \mathbb{N} \text{ with } m ≤ n$$