query: Combinatorial Argument for the following binomial identify
positive_passages.docid: 56828
positive_passages.text: A combinatorial proof that the alternating sum of binomial coefficients is zero
negative_passages.docid: 125220
negative_passages.text: Solving binomial theorem via induction
negative_passages.docid: 68882
negative_passages.text: Path to Combinatorics Problem [$1.11$]
negative_passages.docid: 146810
negative_passages.text: How to derive this binomial identity?
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: 145524
negative_passages.text: Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set
negative_passages.docid: 1139
negative_passages.text: Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
negative_passages.docid: 3786
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$
negative_passages.docid: 133150
negative_passages.text: Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$
negative_passages.docid: 76368
negative_passages.text: Proving the Binomial theorem
negative_passages.docid: 158508
negative_passages.text: Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
negative_passages.docid: 61483
negative_passages.text: Prove the following identity combinatorially
negative_passages.docid: 33104
negative_passages.text: Combinatorial Proof with Summation Identity
negative_passages.docid: 29828
negative_passages.text: Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
negative_passages.docid: 122006
negative_passages.text: Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
negative_passages.docid: 9522
negative_passages.text: Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$