Combinatorial Proof: $ {a \choose b} {b \choose c} = {a \choose a-c}{a-c \choose b-c}$
5149
Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
5801
Combinatorial proof help
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
424
Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
3786
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
34929
Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.
74887
Combinatorial proof of the identity ${n+1\choose k+1}={k\choose k}+{k+1\choose k}+...+{n-1\choose k}+{n\choose k}$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]