Permutation and Combination Calculator
Compute permutations and combinations with exact integer results, including the relation to factorials.
Runs 100% in your browser — nothing is uploaded.
Result
Formula
nCr = n! ÷ (r!(n−r)!) nPr = n! ÷ (n−r)!
About this calculator
Combinations count selections where order does not matter; permutations count ordered arrangements. Choosing 2 from {A,B,C} gives 3 combinations but 6 permutations.
How to use
- 1
Enter n and r.
- 2
Choose what to count.
- 3
Read the exact result.
Frequently asked questions
What is the difference between a permutation and a combination?
A permutation is an arrangement where order matters (e.g., a lock code). A combination is a selection where order does not matter (e.g., a lottery draw).
Can r be greater than n?
No, r must be less than or equal to n. If r > n, the result is 0 because you cannot choose more items than available.
What does 'n!' mean?
n! (n factorial) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
Please note: Results are estimates for general information only and are not professional or medical/financial advice.