Section 3.5 Summary of Permutations and Combinations
In summary, it can be difficult to distinguish whether to use permutations or combinations to solve a counting problem.
The number of ways to choose \(n\) objects from \(n\) available objects,
Ordered, with replacement is \(n^k\text{.}\)
Ordered, without replacement, is \(\nPr{n}{k}\text{.}\)
Unordered, without replacement, is \(\nCr{n}{k}\text{.}\)
Unordered, with replacement, is more complicated.