query: How to prove this equation of combinations?
positive_passages.docid: 8476
positive_passages.text: Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$
negative_passages.docid: 36388
negative_passages.text: How to derive this Combinatorial identity
negative_passages.docid: 48434
negative_passages.text: Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.
negative_passages.docid: 39724
negative_passages.text: Combinatorial Identities
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 38037
negative_passages.text: A problem with my reasoning in a problem about combinations
negative_passages.docid: 67844
negative_passages.text: Prove equation with binomial coefficient
negative_passages.docid: 111951
negative_passages.text: Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
negative_passages.docid: 47799
negative_passages.text: Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
negative_passages.docid: 28936
negative_passages.text: Proving equation with binomial coefficient
negative_passages.docid: 50226
negative_passages.text: Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
negative_passages.docid: 10917
negative_passages.text: Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
negative_passages.docid: 9522
negative_passages.text: Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
negative_passages.docid: 70282
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
negative_passages.docid: 118372
negative_passages.text: Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
negative_passages.docid: 74682
negative_passages.text: How should I solve combination addition like this?
negative_passages.docid: 94580
negative_passages.text: Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$