Prove the following identity combinatorics
65983
Combinatorial proof of binomial coefficient summation identity
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
156564
Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$
107021
Finding a combinatorial argument for an interesting identity: $\sum_k \binom nk \binom{m+k}n = \sum_i \binom ni \binom mi 2^i$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
140140
An identity which applies to all of the natural numbers
26343
Number of certain (0,1)-matrices, Stanley's Enumerative Combinatorics
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"
156566
Combinatorial proof of a binomial identity: $\sum_k \binom {2r} {2k-1}\binom{k-1}{s-1} = 2^{2r-2s+1}\binom{2r-s}{s-1}$
125174
Combinatorial intuition of identity
33104
Combinatorial Proof with Summation Identity
149686
Combinatorics and trigonometry identity
117775
Combinatorial proof of a Stirling number identity.
103347
combinatorial proof of summation
109648
Proving an identity for Bernoulli polynomials