Show that ${n \choose k}{k \choose m} = {n \choose m}{n-m \choose k-m}$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
15733
Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
54442
Sum of $k {n \choose k}$ is $n2^{n-1}$
120074
Prove by Combinatorial Argument that $\binom{n}{k}= \frac{n}{k} \binom{n-1}{k-1}$
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
114911
Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
117761
When is $\binom{n}{k}$ divisible by $n$?
24212
proving how many permutations exist.
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
116913
Whats the difference between the following? $n+k-1 \choose k$ ${{n+k-1}\choose{k-1}}$ ${{n+k-1}\choose{n}}$
925
Prove that $F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$ where $F(n)$ is the $n$-th fibonacci number