Combinatorial Proof of $Q_n = D_n + D_{n-1}$
103854
Showing that $Q_n=D_n+D_{n-1}$
60860
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
5801
Combinatorial proof help
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
41726
Musical and combinatorial proof
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
53263
Show $\sum\limits_{d|n}\phi(d) = n$.
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
15452
Proving determinant product rule combinatorially
79124
Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
156383
Proving a combinatorial identity without double counting