What is a permutation
A permutation (nPr) counts how many different ways you can choose and order r items out of n available, without repeating any of them, using the formula nPr = n! / (n − r)!. Since order matters, swapping the position of two chosen items counts as a different arrangement.
Permutations with repetition
When the same item can be chosen more than once, like the digits of a password or the letters of a license plate, the calculation changes: each of the r positions has n options available, independent of earlier choices, giving nr possible arrangements. Because of that, permutations with repetition grow much faster than permutations without repetition.
Permutations and combinations
The difference between permutations and combinations is order: permutations (nPr) take the order of the chosen items into account, while combinations (nCr) don't. Because of that, for the same n and r, permutations are always greater than or equal to combinations, matching exactly only when r is 0 or 1.
Practical example
A 4-digit numeric password, where each digit can repeat, has 104 = 10,000 possible combinations (permutation with repetition). The podium of a race with 8 competitors, with no repetition and order mattering, has P(8,3) = 336 possible outcomes.