Method
Without repetition, nPr=n!/(n−r)! and nCr=n!/[r!(n−r)!]. With repetition, ordered count is n^r and unordered count is C(n+r−1,r).
Math worksheet
Permutation and Combination Calculator
Count ordered and unordered selections, with or without repetition, using exact arbitrary-size integers.
The calculation runs locally. Exact-integer tools avoid floating point; decimal and transcendental tools report rounding limits.
Method and verification guide
How the Permutation and Combination Calculator works
Without repetition, nPr=n!/(n−r)! and nCr=n!/[r!(n−r)!]. With repetition, ordered count is n^r and unordered count is C(n+r−1,r). The calculator keeps the intermediate values visible so you can reproduce the answer independently.
Interpret the result
Order distinguishes arrangements from groups; repetition determines whether an item can occupy more than one selected position.
Check the assumptions
Items are assumed distinguishable; this does not count permutations of multisets containing identical objects.
Local calculation
Everything runs in this browser. Inputs are not sent to an external calculator.
Rounding
Displayed values may be rounded for readability while calculations use full floating-point precision unless the tool explicitly uses exact integers.
Scope
Items are assumed distinguishable; this does not count permutations of multisets containing identical objects.
Simple by design
Three steps to a clearer number.
Enter your details
Use realistic values in each field. You can change them anytime.
Calculate instantly
The formula runs locally, so there is no account or waiting time.
Use the result
Treat the answer as a practical estimate for your next decision.