Permutation & Combination Calculator (nPr, nCr)
Calculate permutations (nPr) and combinations (nCr) — order matters vs doesn't.
What this calculates
Permutations count ordered arrangements (passwords, race finishes). Combinations count unordered selections (lottery, committee picks). The difference matters: 5-letter passwords have many more permutations than the 5-letter subsets you can pull from the alphabet.
Formula & how it works
Permutations: nPr = n! / (n−r)!. Combinations: nCr = n! / (r!(n−r)!). Always nCr ≤ nPr, with nPr = nCr × r!.
Worked example
n=10, r=3. nPr = 720 (ordered podium finishes from 10 racers). nCr = 120 (3-person committees from 10 candidates).
Frequently asked questions
When is order important?
Whenever swapping two picks creates a different outcome — race rankings, password characters, seat assignments.
Lottery odds?
Combination. 'Pick 6 from 49' = 49C6 = 13,983,816. Your odds of winning the jackpot are 1 in that number.
What is 0!?
By convention, 0! = 1 — required for the formulas to behave consistently.