Combinations & Permutations Calculator
Enter n and r to get combinations (nCr) and permutations (nPr).
Count the ways, ordered or not
Probability and combinatorics constantly ask how many ways you can choose or arrange things. Permutations (nPr) count arrangements where order matters; combinations (nCr) count selections where it does not. Enter n and r to get both at once.
Choosing 3 from 10, there are 720 ordered permutations but only 120 unordered combinations — the same selection counted with and without order. Seeing them side by side makes the distinction concrete.
Accurate and private
Instead of computing giant factorials, it multiplies the ratio term by term, which stays exact for much larger inputs. The math runs entirely in your browser.
Frequently Asked Questions
What is the difference between nCr and nPr?
Permutations (nPr) count ordered arrangements; combinations (nCr) count unordered selections. nPr is always at least as large as nCr.
How does it avoid overflow?
It multiplies and divides step by step instead of computing full factorials, so large n and r stay accurate far longer.
What are the formulas?
nPr = n! / (n−r)! and nCr = n! / (r!(n−r)!). Both require 0 ≤ r ≤ n.
Browse the full set of free, private, in-browser tools.