One Binomial Equation $\sum_{i=0}^{z} {n_1 \choose i}{n_2 \choose z-i} = {n_1+n_2 \choose z}$
42763
How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$?
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
156873
Solve the equation $\binom{2n+1}{n+2} = \binom{2n+1}{5} $
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
142994
How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
28027
Find $\sum_{k=0}^{n}4^k \binom{n}{k}$
8806
Summation of binomial coefficients
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$