Help with proving this combinatorial identity?
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
108688
An identity involving products of sums
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
129304
Alternative combinatorial proof for $\sum\limits_{r=0}^n\binom{n}{r}\binom{m+r}{n}=\sum\limits_{r=0}^n\binom{n}{r}\binom{m}{r}2^r$
150281
Am I on the right track to figure out this combinatorics problem?
46132
Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?
133150
Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
55481
Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$
103347
combinatorial proof of summation
149686
Combinatorics and trigonometry identity
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
10875
proof of binomial identity involving double sum
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$