Prove that this sum of products of binomial coefficient can be simplified like this
126001
Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
108688
An identity involving products of sums
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
33104
Combinatorial Proof with Summation Identity
55481
Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$
67844
Prove equation with binomial coefficient
47052
How can I simplify this expression involving binomial coefficients?
10875
proof of binomial identity involving double sum
107335
Prove equality between binomial coefficients.
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
48434
Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.
143945
Summation of combination of binomial coefficient