Prove a combinatorial identity with a combinatorial argument
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
50250
Proving $\arg(zw)=\arg(z)+\arg(w)$
27585
Combinatorial proof of Stirling Number Identity (First Kind)
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
17580
Combinatorics That Looks Similar to Vandermonde's Identity
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
55481
Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
32780
Combinatorial Proof Question: Vandermonde convolution identity
48434
Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.
103347
combinatorial proof of summation
39724
Combinatorial Identities
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$