Sum of products of binomial coefficients is equal to another binomial coefficient
46132
Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
143945
Summation of combination of binomial coefficient
14986
Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
126214
Multiplying Binomial Terms
122024
Asymptotic of a sum involving binomial coefficients
61270
Binomial Theorem Sum
45672
Even/Odd Binomial Coefficients
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
132249
Sum of every $k$th binomial coefficient.
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$