Pascal's Identity states that for any non-negative integers $n$ and $k$, the binomial coefficient can be expressed as $$\binom{n}{k} = \binom{n-1}{k-1} + \binom{n-1}{k}$$. This identity is crucial in combinatorial proofs as it provides a way to break down complex binomial coefficients into simpler components, helping in the derivation of other identities and properties in combinatorics.
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