A Proof in Combinatorics
94580
Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
113290
Prove combinatorics identity
42062
Interpretation of a combinatorial expression
103538
Partitions of $n$ into distinct odd and even parts proof
112573
Combinatorial proof for Stirling number of 1st kind's generating function
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
82872
Combinatorial proof involving partitions and generating functions
14986
Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
41205
Help me solve a combinatorial problem
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
125174
Combinatorial intuition of identity
103106
Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
74887
Combinatorial proof of the identity ${n+1\choose k+1}={k\choose k}+{k+1\choose k}+...+{n-1\choose k}+{n\choose k}$
48434
Prove that $\sum\limits_{k=0}^m\binom{m}k\binom{n}{r+k}=\binom{m+n}{m+r}$ using combinatoric arguments.