Is there any combinatorial argument to show the given result?
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
111954
Computing the cardinality of a combinatorial set
139842
Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^2\binom{n}{k}=n\times 2^n$
65983
Combinatorial proof of binomial coefficient summation identity
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
156383
Proving a combinatorial identity without double counting
61268
Is there a combinatorial interpretation of the triangular numbers?
94784
$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
48434
Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.
152084
Binomial-Theorem proof
90904
Combinatorial proof of an identity with squared binomial coefficients
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
97254
What is the proof of permutations of similar objects?
86263
How do we show there are the same number of elements in each of the sets?
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
2251
Can someone give me a hint on how to prove this?
33104
Combinatorial Proof with Summation Identity