What is the formula for permutation with repetition?

The formula is n^r, where n is the total number of objects and r is the sample size, meaning each of the r positions can be filled by any of the n objects.

Can this calculator handle large numbers of objects?

The tool restricts input to a maximum of 10 objects and a sample size of 10, so very large sets exceed its limits.

How does this differ from permutation without repetition?

Permutation with repetition allows items to be reused in the arrangement, while permutation without repetition requires each item to be unique and used only once.

What kinds of real-world problems is this used for?

Common uses include calculating possible PIN codes, password combinations, or any scenario where items can repeat in the order.

StatisticsFree Tool

Permutation with Repetition Calculator

Provided byOmni Calculatoromnicalculator.com

Find out how many different arrangements of a set of objects are possible using this permutation with repetition calc...

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About this tool

What Permutation with Repetition Calculator does

A permutation with repetition calculator determines the number of distinct arrangements when objects can be reused. It takes a total number of objects and a sample size to compute arrangements where items may appear multiple times, such as 4-digit pins using digits 0-9. The output shows the total count of possible permutations and can also list every arrangement. The site provides the underlying formula, explains the concept of permutations versus permutations with repetition, and includes a practical example to help users understand the math before using the tool.

Step by step

How to use the Omni Calculator Permutation with Repetition Calculator

1
Enter the total number of objects (n) in the first field
2
Enter the sample size (r) — how many items appear in each arrangement — in the second field
3
The calculator displays the total number of permutations with repetition
4
Use the additional option to generate and list all individual permutations if needed

Is it right for you

Best for

This tool suits beginners and students learning probability, as well as anyone needing quick arrangements for codes, pins, or repeated-item scenarios without manual counting.

Limitations

Results grow exponentially with larger n and r values
No unit conversion or unit switching supported
Calculator limits input to n = 10 and r = 10, restricting very large sets

Questions

Permutation with Repetition Calculator FAQ

What is the formula for permutation with repetition?: The formula is n^r, where n is the total number of objects and r is the sample size, meaning each of the r positions can be filled by any of the n objects.
Can this calculator handle large numbers of objects?: The tool restricts input to a maximum of 10 objects and a sample size of 10, so very large sets exceed its limits.
How does this differ from permutation without repetition?: Permutation with repetition allows items to be reused in the arrangement, while permutation without repetition requires each item to be unique and used only once.
What kinds of real-world problems is this used for?: Common uses include calculating possible PIN codes, password combinations, or any scenario where items can repeat in the order.

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