Permutation & Combination Calculator
Count selections exactly using integer arithmetic. Decide whether order matters and whether a choice can be repeated. One page handles both combinations and permutations so you can compare the assumptions before treating a result as a probability.
Your result
How the calculation works
Without repetition: P(n,r)=n!/(n−r)!, C(n,r)=n!/[r!(n−r)!]. With repetition: ordered n^r; unordered C(n+r−1,r). Selecting zero items has one arrangement.
Worked example
Choosing three different items from ten without order gives C(10,3)=120. Ordered selections give P(10,3)=720. Ordered selections with replacement give 10³=1,000.
Assumptions and limitations
n and r are whole numbers from 0 to 10,000. Without replacement r≤n. Items are distinguishable; constraints, capacities and unequal probabilities are not modeled. Large answers remain exact integers.
A count becomes a probability only after defining equally likely outcomes and a compatible favorable-outcome count. This tool does not infer those assumptions from the numbers alone.
Sources and editorial responsibility
Maintained by Renvoro Pty Ltd. Sources inform the methods and assumptions shown here; outputs have the limitations described on this page.
Method reviewed 2026-10-13. Calculation standards · Report an issue