Choose 3 from 10
10P3 and 10C3720 permutations, 120 combinations
Permutation and Combination Calculator
Use this free permutation and combination calculator to find exact nPr and nCr counts, compare order-matters and group-selection problems, and check the formula steps.
Inputs to checkExample numbersCopyable answerTab-only history
n=10, r=3120 combinations
- nPr
- 720
- nCr
- 120
- Order matters
- Permutation
- Order does not matter
- Combination
Recent answers
Recent answers will appear here.
Input tips
Use permutations when order matters.
Use combinations when order does not matter.
How to use the Permutation and Combination Calculator
- Enter n for the total items and r for the items selected.
- Press Calculate nPr and nCr to see permutation and combination counts.
- Use nPr when order matters and nCr when order does not matter.
- Review the formulas, examples, recent answers, and exact integer output.
What people use it for
Find permutations for rankings, podium finishes, codes, or ordered choices.
Find combinations for committees, card hands, teams, or unordered groups.
Compare nPr and nCr from the same n and r before choosing a probability denominator.
Copy exact integer nPr and nCr results for notes, homework, or study checks.
Quick examples
Cards example
52C52,598,960 combinations
Podium order
8P3336 permutations
Four-person committee
12P4 and 12C411,880 permutations, 495 combinations
Two finalists
5P2 and 5C220 permutations, 10 combinations
Three-letter ordered code
26P3 and 26C315,600 permutations, 2,600 combinations
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Permutation and Combination CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
- All free toolsSearch every live tool, converter, calculator, AI helper, and browser utility.
Frequently asked questions
Quick answers about formulas, inputs, examples, result copying, and private in-browser history.
What is a permutation?
A permutation counts arrangements where order matters. ABC and BAC are different permutations.
What is a combination?
A combination counts selections where order does not matter. ABC and BAC are the same combination.
What do the main Permutation and Combination Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Permutation and Combination Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What do n and r mean?
n is the total number of available items. r is how many of those items are selected or arranged.
What formulas does the calculator use?
It uses nPr = n! / (n - r)! for permutations and nCr = n! / (r! x (n - r)!) for combinations.
What does factorial mean?
A factorial multiplies whole numbers downward. For example, 5! = 5 x 4 x 3 x 2 x 1. The calculator also treats 0! as 1, which is standard for these formulas.
What input range is supported?
This calculator supports whole-number n values from 0 to 500 and r values from 0 to n.
Can r be zero in this calculator?
Yes. There is exactly one way to choose or arrange nothing, so both nP0 and nC0 equal 1.
Does this allow repeats or replacement?
No. This calculator uses the standard no-replacement nPr and nCr formulas. If an item can be reused, you need a replacement-based counting method.
Why is nPr usually larger than nCr for the same n and r?
nPr counts every order separately. nCr groups those ordered arrangements together by dividing by r!, so ABC, ACB, BAC, BCA, CAB, and CBA count as one combination.
How does this connect to probability?
Many probability problems use combinations or permutations to count favorable outcomes and total possible outcomes.
What should I double-check before using the answer?
Check whether order matters, whether repeats are allowed, whether every item is distinct, and whether the problem asks for arrangements, selections, or a probability built from those counts.
Is my counting history private?
Yes. Recent nPr and nCr answers stay only in the current browser tab while you use the page. They are not sent to a server.