How the Permutation & Combination Calculator works.
nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!)n is the total number of distinct items and r is the number selected without replacement.
Worked example for the Permutation & Combination Calculator.
Selecting 2 people from 5 gives 20 ordered permutations but 10 unordered combinations.
How to read this result.
Choose nPr when position matters and nCr when the selected group is the outcome; both require r no greater than n.
How the calculation works
Permutations count ordered selections: nPr = n!/(n−r)!; combinations ignore order: nCr = n!/(r!(n−r)!). Formula or rule: nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!). n is the total number of distinct items and r is the number selected without replacement.
What this calculator does not prove
The formulas assume distinct selectable items and no replacement. Repeated objects, replacement, restrictions, and conditional arrangements require a different model. Use the result for the mathematical question shown here; a correct calculation does not by itself establish that the source data, sample, or real-world assumption is appropriate.
Inputs and edge cases to check.
n and r must be whole numbers with 0 ≤ r ≤ n; values are limited to keep exact integer results displayable. Decide whether different orders count as different outcomes before choosing permutation or combination mode, since that choice changes the result.
What this tool does not include.
The formulas assume distinct selectable items and no replacement. Repeated objects, replacement, restrictions, and conditional arrangements require a different model.
Reference guidance and methodology.
Permutation & Combination Calculator questions.
What does the Permutation & Combination Calculator calculate?
Calculate nPr when order matters or nCr when it does not, using exact integer arithmetic.
Which formula or algorithm does it use?
nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!). n is the total number of distinct items and r is the number selected without replacement.
What limitations or edge cases matter?
n and r must be whole numbers with 0 ≤ r ≤ n; values are limited to keep exact integer results displayable. Decide whether different orders count as different outcomes before choosing permutation or combination mode, since that choice changes the result. The formulas assume distinct selectable items and no replacement. Repeated objects, replacement, restrictions, and conditional arrangements require a different model.