Combinatorial Proofs with Summation
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
82872
Combinatorial proof involving partitions and generating functions
48434
Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.
84010
Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even
96585
Sums and permutation
72402
Summation of natural number set with power of $m$
39724
Combinatorial Identities
145900
Proof of a double summation reduction identity
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
156383
Proving a combinatorial identity without double counting
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
60860
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
107964
Simple combinatorics problem.
152911
Stirling numbers combinatorial proof
26790
Proving the geometric sum formula by induction
59831
How to relate combinatorial proof to bipartite graphs?