How to derive this Combinatorial identity
7063
How to compute the  formula $\sum  \limits_{r=1}^d r \cdot 2^r$?
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
3786
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
105237
Alternating sum of binomial coefficients identity
59638
How to prove this result on binomial coefficients?
39724
Combinatorial Identities
46132
Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?
33104
Combinatorial Proof with Summation Identity
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
154703
Use combinatorics to prove $L\left(n,k\right)=\sum_{j=0}^{n}{ n\brack j}{j\brace k}$
45725
Derivation of an identity with beta function.
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
71564
Combinatorial proof of identity involving central binomial coefficients
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$