Count arrangements of objects, distinguishing whether order matters.
Permutation and Combination Calculator
Form
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Table of Contents
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What is Permutation and Combination?
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How to Use This Calculator
- Enter or select Total number of objects n, Sample size r.
- Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
- Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used
Ordered: P(n,r)=n!/(n−r)!; unordered: C(n,r)=n!/(r!(n−r)!)
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Variables Explained
| Input | What it means |
|---|---|
| Total number of objects n | The number to test or transform; use the integer or real-number domain stated in the formula. |
| Sample size r | Number of observations or responses in the sample, rather than the population size. |
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Worked Example
Selecting 2 of 5 gives 20 ordered arrangements or 10 unordered pairs.
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Why Use This Calculator?
Compare the number of ordered arrangements with unordered groups.
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Common Mistakes
- These formulas assume objects are distinct and cannot be reused.
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Frequently Asked Questions
Should I round numbers before calculating?
Keep the original input precision through the calculation and round the final answer to the precision you need. Rounding an intermediate result can change later steps.
Why can a manual calculation differ slightly?
Check the operation, units, signs and rounding first. Equivalent fractions or expressions can look different while representing the same value.
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Sources & References
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