I have trouble solving combinatorics proofs. I've looked at a bunch of textbook examples, but I never seem to figure out how to solve one on my own.
Right now, I am stuck with this one:
$\binom{3k}{k}$ = $\sum_{i=0}^{k} \binom{k+i}{k}\binom{2k-1-i}{k-1}$
I've been thinking maybe I can do something with the LHS being the collection of binary-strings with k 1's and 2k 0's,
So that would mean the RHS has to partition that in someway, I've seen solutions partitioning according to last occurence of a 1, or according to the number of 1's, positions in the string. But none of these seem applicable here.
Hints appreciated