Math & science
Permutation Combination Calculator
Calculate nPr and nCr for selecting and arranging r items from a total of n items.
Interactive calculator
Calculate nPr and nCr
Compare permutations and combinations for choosing r items from a set of n items.
Results
Permutation (nPr)
720
Combination (nCr)
120
How to use it
- 01Enter n for the total number of items.
- 02Enter r for the number of items chosen.
- 03Review both the permutation and combination result to compare ordered versus unordered counting.
Result guide
- n and r are treated as whole-number counts in this version.
- r cannot be larger than n for a valid selection setup.
- Permutation counts arrangements, while combination ignores order.
About this calculator
Permutation and combination pages are common in probability, school math, and entrance-exam prep because students routinely need both formulas side by side.
Keeping nPr and nCr together is important because many users mix them up and need a quick comparison of ordered versus unordered selection.
Frequently asked questions
What is the difference between nPr and nCr?
nPr counts ordered arrangements, while nCr counts selections where order does not matter.
Why must r be less than or equal to n?
Because you cannot choose more items than actually exist in the set.
Why keep both answers on one page?
Because many users solve probability and counting problems by comparing whether order matters before choosing the right formula.
Method and limitations
This calculator uses the formula and assumptions described on this page. We do not claim independent professional review. Direct references will be listed here when they support a specific rule or data source used by this calculator.
Results are estimates for general information. Verify current rules and assumptions before making financial, tax, or health decisions.
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