List questions from combinatorial-proofs | MathQa

Prove using a combinatorial argument the following statement: $\binom{n+m}{2} = \binom{m}{2} + \binom{n}{2} + \binom{n}{1}\binom{m}{1}$

Published on 01 Jan 2025 - 19:39

Can we simplify this factorial summation $\sum_{i=0}^{n-1} i!(n-i)!$?

Published on 01 Jan 2025 - 9:39

Deduce formula for $\sum_{j=0}^m {m \choose j}(-1)^j j^{m+1}$

Published on 02 Jan 2025 - 15:56

Prove that if four numbers are chosen from the set $\{1,2,3,4,5,6\}$, at least one pair must add up to $7$.

Published on 01 Jan 2025 - 16:30

Need help in following problems related to combinatorial analysis.

Published on 21 Dec 2024 - 10:37

Prove combinatorial Identity using a combinatorial argument.

Published on 01 Jan 2025 - 23:51

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Published on 30 Dec 2024 - 12:55

Prove this binomial identity using the following equality:

Published on 01 Jan 2025 - 15:36

Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^3\binom{n}{k}=0$

Published on 05 Jan 2025 - 15:24

Combinatorial Proof for the Identity $\sum_{k=0}^n \binom{n}{k}\left(-2\right)^k = (-1)^n$

Published on 02 Jan 2025 - 6:11