New posts in combinatorial-proofs

Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$

combinatorics binomial-coefficients combinatorial-proofs

Two interview questions

combinatorics algebra-precalculus proof-verification combinatorial-proofs

Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$

combinatorics binomial-coefficients combinatorial-proofs

Combinatorial argument to prove the recurrence relation for number of derangements

combinatorics recurrence-relations inclusion-exclusion combinatorial-proofs derangements

Combinatorial interpretation of sum of squares, cubes

combinatorics summation combinatorial-proofs

The Hexagonal Property of Pascal's Triangle

combinatorics binomial-coefficients alternative-proof combinatorial-proofs

Evaluate $\sum\limits_{k=1}^n k^2$ and $\sum\limits_{k=1}^n k(k+1)$ combinatorially

combinatorics summation binomial-coefficients combinatorial-proofs

Combinatorial identity $\sum_{k=0}^{n}\binom{n}{k}\binom{n}{k -1} = \binom{2n}{n+1}$

combinatorics discrete-mathematics summation binomial-coefficients combinatorial-proofs

Finding a closed formula for $\sum_{r=0}^k {k \choose r}{k \choose r-1}$

combinatorics summation binomial-coefficients combinatorial-proofs

Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.

combinatorics summation binomial-coefficients combinatorial-proofs

What is $\binom{n}{2} \binom{n}{1} + \binom{n}{3} \binom{n}{2} + \ldots + \binom{n}{n-1} \binom{n}{n-2} + \binom{n}{n} \binom{n}{n-1}$?

probability combinatorics summation binomial-coefficients combinatorial-proofs

Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?

combinatorics summation binomial-coefficients combinatorial-proofs

Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even

combinatorics binomial-coefficients combinatorial-proofs

Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$

combinatorics summation binomial-coefficients convolution combinatorial-proofs

Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$

combinatorics summation binomial-coefficients combinatorial-proofs