Practice: Category 2 of Combinations

What is a combinatorial proof?

State Pascal's Identity.

What does a combinatorial proof primarily focus on?

Is it true that Pascal's Identity can be expressed as $\binom{n+1}{k} = \binom{n}{k} + \binom{n}{k-1}$?

Prove that $\binom{n}{k} + \binom{n}{k-1} = \binom{n+1}{k}$ using combinatorial reasoning.

Provide a combinatorial proof for the identity $\binom{n}{k} = \binom{n}{n-k}$ and explain its significance.