When to use this calculator
Count ordered codes or sequences when choices can repeat. All positions have the same independent set of available choices.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Polynomial Derivative Calculator: Find the slope of a cubic polynomial at a chosen input.
PUTTING IT INTO PRACTICE
Permutation With Repetition: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Choices per position (integer) | 10 |
| Positions (integer) | 4 |
| Result | 10,000 ways |
- Check the input labels and enter the example values above.
- Apply the relationship: Ordered sequences = choices^positions.
- The result is 10,000 ways, rounded for display.
How to interpret your result
All positions have the same independent set of available choices.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the permutation with repetition calculator useful?
Count ordered codes or sequences when choices can repeat. All positions have the same independent set of available choices.
How do I use the permutation with repetition calculator?
Enter choices per position (integer), positions (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Ordered sequences = choices^positions.
What should I check before using the result?
All positions have the same independent set of available choices.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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