Question

I wish to order h hats from a store which sells k different kinds of hats. By balls-in-urns, I know that this is the same as \[{{h+k-1} \choose h}\].
Question: Use partitioning to show that this is the same as \[\sum_{r=1}^k {k \choose r}{{h-1} \choose {r-1}}\].

Answer 1

PS: I also want to know how to not put an equation on its own line.