Simplest Non-trivial exmaple from combinatorics

Question

I'm listening to a lecture on probability and this expression comes up $\binom{n+k-1}{k}$ and it supposedly denotes the number of ways to put $k$ indistinguishable particles into $n$ distinguishable boxes but in an example where the instructor sets $n=2$, he then states the answer becomes $\binom{k+1}{k}.$ I just need some logical narrative to understand how $2$ went missing. Thanks in advance.