Stars and Bars Reference

Question

Essentially what stars and bars framework allows us to do is to draw one to one correspondents between sets $$\left\{ (x_1,x_2,\ldots ,x_n)\; \colon \; \sum_{i=1}^nx_i=t, \ x_1,x_2,\ldots ,x_n\in \mathbb{N}_0 \right\}$$ and $$\left\{ (k_1,k_2,\ldots ,k_{n-1}) \; \colon \; k_1 < k_2 < \ldots < k_{n-1} < t+n,\ k_1,k_2,\ldots ,k_{n-1}\in \mathbb{N}\right\}.$$ I.e. between integer sums to $t$ and possible configurations of "bars". Are there books that cover this topic rigorously? I'm looking for a reference for this one to one correspondents.

Answer 1

According to Wikipedia, which is, imo, pretty good on this subject, stars and bars was popularized in William Feller's classic book on probability.