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View All Online ConvertersPermutation Combination Calculator
Calculate permutations and combinations online, compare nPr and nCr, and review the exact result, formula, and order rule.
Calculate permutations and combinations
Enter total items and selected items, then switch between combination and permutation mode to compare nCr and nPr results.
Compare nCr and nPr with one focused combinatorics calculator
Use this permutation and combination calculator when you need to count selections, groups, or arrangements for homework, probability practice, interview prep, or quick combinatorics checks in the browser.
Enter n and r to calculate an exact result.
Permutation or combination result
Review the exact result first, then check the notation, formula, input values, and order rule.
Ready
Enter values to compare nCr and nPr.
The result will show the exact permutation or combination count for the current mode.
How to use the permutation combination calculator
- Choose Combination (nCr) if order does not matter, or Permutation (nPr) if order matters.
- Enter the total number of items as `n`.
- Enter the number of selected items as `r`.
- Review the exact result, notation, and symbolic formula for the current mode.
- Use the order-rule card to confirm whether the mode counts unordered selections or ordered arrangements.
Permutation and combination calculator examples
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10 choose 3
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10 P 3
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how many combinations of 5 items choose 2
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ncr and npr calculator
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how many ways to choose 3 from 10
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permutation of 10 items taken 3 at a time
What this permutation combination calculator covers
This tool calculates both combinations and permutations from one pair of whole-number inputs. It gives you the exact count, the matching `nCr` or `nPr` notation, the symbolic formula, and a clear order-matters explanation so you can compare the two ideas without switching pages.
Combination vs permutation
A combination counts how many ways you can choose items when order does not matter. A permutation counts how many ordered arrangements are possible when order matters. That is why `10C3` and `10P3` use the same inputs but return different answers.
When this calculator is useful
A permutation and combination calculator is useful for probability questions, card hands, seating arrangements, selection problems, classroom combinatorics, and interview-style counting tasks. If you are unsure whether to use `nCr` or `nPr`, compare both modes with the same `n` and `r` values.
Permutation and combination calculator FAQs
What is the difference between combination and permutation?
A combination ignores order, while a permutation counts different orders as different outcomes. Use combination when the group itself matters, and permutation when the arrangement matters.
What does nCr mean?
`nCr` is the number of combinations of `r` items chosen from `n` total items. It is used when order does not matter.
What does nPr mean?
`nPr` is the number of permutations of `r` items chosen from `n` total items. It is used when order matters.
Why does the calculator show 10C3 or 10P3?
This tool uses the compact `nCr` and `nPr` notation in the result area, such as `10C3` or `10P3`. These mean the same thing as `C(10,3)` and `P(10,3)`.
Can r be greater than n?
No. In permutation and combination problems, `r` cannot be greater than `n` because you cannot choose or arrange more items than the total number available. This calculator requires `r` to be less than or equal to `n`.
Is 0 choose 0 equal to 1?
Yes. In combinations, `0 choose 0` is defined as 1 because there is exactly one way to choose nothing from nothing: choose the empty set.
Does this calculator return exact answers?
Yes. The tool uses exact whole-number arithmetic for supported inputs, so the result is not rounded.