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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.
Reviewed by Dr. Elena Rostova, MD, PhD
Medical Doctor & Clinical Nutrition Researcher
Reviews health index calculators, unit converter benchmarks, and mathematical models against WHO guidelines and peer-reviewed research.
Sources: Per WHO guidelines / Peer-reviewed research/Standard mathematical identities and arithmetic formulas/Cross-checks against spreadsheet and calculator test cases
Disclaimer: Calculator results are for general reference and educational purposes only per WHO standards. Health indexes and mathematical models are not a substitute for professional medical diagnosis, clinical nutrition, or certified trade advice.
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