query: Evaluate the following sum using a combinatorial argument
positive_passages.docid: 30472
positive_passages.text: Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
negative_passages.docid: 147766
negative_passages.text: Sum of Permutations from 0 to n
negative_passages.docid: 76828
negative_passages.text: Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
negative_passages.docid: 91933
negative_passages.text: Evaluate $\sum_{k=1}^nk\cdot k!$
negative_passages.docid: 92784
negative_passages.text: Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
negative_passages.docid: 96585
negative_passages.text: Sums and permutation
negative_passages.docid: 39724
negative_passages.text: Combinatorial Identities
negative_passages.docid: 150281
negative_passages.text: Am I on the right track to figure out this combinatorics problem?
negative_passages.docid: 143945
negative_passages.text: Summation of combination of binomial coefficient
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 130083
negative_passages.text: Evaluating sum of a combination series
negative_passages.docid: 61417
negative_passages.text: List of numbers giving a particular sum
negative_passages.docid: 140877
negative_passages.text: Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
negative_passages.docid: 107021
negative_passages.text: Finding a combinatorial argument for an interesting identity: $\sum_k \binom nk \binom{m+k}n = \sum_i \binom ni \binom mi 2^i$
negative_passages.docid: 57549
negative_passages.text: Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
negative_passages.docid: 31970
negative_passages.text: Alternating sum of squares of binomial coefficients
negative_passages.docid: 19571
negative_passages.text: Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$