Compute permutations nPr for ordered selections of r items from n, plus the with-repetition count n^r.
Permutations nPr
How to use this tool
Enter the total number of items.
Enter how many items are arranged.
Read the ordered count without repetition.
Compare with the n^r count when repeats are allowed.
Formula & worked example
10P3 = 720 ordered ways to pick 3 items from 10; with repetition allowed the count would be 10³ = 1,000.
Limitations — read this before you rely on it
Whole numbers only, n at most 170; this tool counts ordered selections and does not compute combinations.
Frequently asked questions
An ordered arrangement: swapping two chosen items gives a different permutation.
Combinations ignore order, so they are fewer; this tool counts ordered selections only.
Items may be reused, as in a PIN code where digits can repeat, giving n^r possibilities.
There is exactly one way to choose nothing, by the empty-arrangement convention.
Not without repetition: you cannot pick more distinct items than exist, so the tool reports an error.