Show by combinatorial proof that for $n \geq 4$, $3 {n \choose 4} + 3{n\choose 3} = {{n \choose 2} \choose 2}$
61483
Prove the following identity combinatorially
90519
Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
71534
Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
24212
proving how many permutations exist.
146867
Combinatorial Proof Of A Number Theory Theorem--Confusion
14986
Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
113290
Prove combinatorics identity