Prove $\sum_{i=0}^k (-1)^{k-i} {n \choose i} {n-i-1 \choose k-i}=1$. I was recently working through the proof of a question using inclusion exclusion and was stuck on this part. I verified this equation with wolfram alpha.
2026-04-05 23:28:31.1775431711
Why is $\sum_{i=0}^k (-1)^{k-i} {n \choose i} {n-i-1 \choose k-i}=1$
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