Overview
What Are Permutations and Combinations?
Permutations count arrangements where order matters (nPr); combinations count selections where order doesn't matter (nCr).
Calculate permutations and combinations instantly.
Permutations count arrangements where order matters (nPr); combinations count selections where order doesn't matter (nCr).
Useful for probability, statistics, and combinatorics coursework.
Input the total number of items available.
Input how many items you're selecting.
Permutation and combination values update automatically.
nPr = n! ÷ (n-r)!
nCr = n! ÷ (r! × (n-r)!)
Use permutation when order matters (like arranging items); use combination when only the selection matters, not order.
No, you can't select more items than are available - r should be less than or equal to n.
Arranging people in a line, or determining possible race finishing orders.
Selecting a committee from a group, or choosing lottery numbers where order doesn't matter.
No, calculations happen entirely in your browser.
nP0 and nC0 both equal 1 by mathematical convention (there's exactly one way to choose nothing).
Yes, for the same n and r (when r>1), since combination doesn't count different orderings as separate.
Yes, completely free with no sign-up required.