Using the calculator
Type n, the number of things available, then r, how many places to fill, such as 10, 3. The count appears as you type, with the combination count beside it.
Set Repeats to Allowed when an item can be used again, as with the digits of a PIN.
The nPr formula
nPr = n! / (n − r)!. For 10 runners and 3 medals, the gold can go to any of 10, the silver to any of the 9 left and the bronze to any of the 8 after that, which makes 10 × 9 × 8 = 720.
With repeats allowed each place has all n choices, so the count is n^r. A 4-digit PIN has 10^4 = 10,000 possibilities.
Questions
When does order matter?
When swapping two items makes a different result, as in a race finish, a password or a seating plan. If only the group matters, as with a committee, use the [combination calculator](/combination-calculator).
What is nPn?
It's n!, every item arranged. 5P5 is 5! = 120.
Why is nPr bigger than nCr?
Each group of r items can be put in r! orders. nPr counts all of them, nCr counts each group once, so nPr = nCr × r!.
Sources
Added and reviewed . What's new