Worked example: Permutation and Combination Calculator
Ten choose three. This fixed reference example shows one complete scenario; the interactive results above use your current inputs.
View the example inputs
- Items n
- 10
- Selected items r
- 3
| Calculated quantity | Example result |
|---|---|
| Permutations | 720 |
| Combinations | 120 |
Working with integers, exact values and numerical representation
Keep integer arithmetic and decimal approximation separate
Factors, divisibility and many counting formulas require whole numbers. A decimal approximation to a fraction is a different representation from the exact fraction. Very large integers can also exceed the range in which ordinary floating-point numbers distinguish every neighboring integer.
Where a tool states that it uses exact integer or decimal arithmetic, read the supported operation and size limits. An integer division can return a quotient and remainder, while a decimal division can produce a truncated expansion. Neither should be mistaken for rounding unless the method says so.
Use the right base and notation
Binary, hexadecimal, Roman and ordinary decimal inputs follow different symbol conventions. A numeral can be valid in one representation and invalid in another. Leading signs, fractional parts and exponent notation are supported only when the form describes them.
Use the worked example to check the representation of both the input and output. A sequence tool follows the explicit rule you choose; a finite list does not identify a unique hidden pattern.
Formula and calculation method
P(n,r)=n!/(n−r)!; C(n,r)=n!/[r!(n−r)!]. Order matters for permutations.
Reference Sources
Frequently asked questions
How does this calculator work?
P(n,r)=n!/(n−r)!; C(n,r)=n!/[r!(n−r)!]. Order matters for permutations.
What assumptions should I check?
Check the units and definitions shown beside each input. Results use the values you enter.
Can I save or print this calculation?
Use Copy link with inputs to reproduce the scenario, Download results for a text record, or Print. Where a schedule is shown, its CSV download includes every row.