Permutation and Combination Calculator — Free Online Calculator
Calculate permutations (nPr) and combinations (nCr) with step-by-step factorial breakdown. Toggle between order matters vs.
Permutations & Combos
Results below
Enter Values
Type
Permutation
Formula
P(5,3) = 5! / (5 − 3)!
Formula Applied
5! / 2! = 120 / 2 = 60
n!
120
r!
6
(n−r)!
2
Scenario Comparison
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Type
Permutation — Order Matters
Each different ordering counts as a unique arrangement.
Permutations for n = 5
The highlighted bar (at r = 3) shows the current selection. Other bars show nPr for all possible r values.
Formula
P(n,r) = n! / (n−r)!
Step-by-Step
5! / 2! = 120 / 2 = 60
n!
120
r!
6
(n−r)!
2
Quick Comparison
Permutations count arrangements where order matters (like passwords or race results).
Combinations count selections where order does not matter (like lottery tickets or committee members).
The combination formula divides by r! to remove duplicate orderings.
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