Help Show Binomial Identity: $\sum_{j=0}^{n} {n \choose j}{m+j \choose n} = \sum_{j=0}^{n} {n \choose j}{m \choose j}2^j$
Finding a combinatorial argument for an interesting identity: $\sum_k \binom nk \binom{m+k}n = \sum_i \binom ni \binom mi 2^i$