Here is a convenient way to arrange the results that we have discussed thus far (and extend our knowledge to cover more ground), from [Blitzstein and Hwang](https://bookdown.org/probability/beta/counting.html#ref-BH). | | **Order Matters** | **Order Doesn’t Matter** | | ----------------------- | ----------------- | ------------------------ | | **With Replacement** | $n^k$ | $\binom{n + k - 1}{k}$ | | **Without Replacement** | $\frac{n!}{(n−k)!}$ | $\binom{n}{k}$ |