# Permutation with Replacement Calculator

The Permutation with Replacement Calculator is a tool that can be used to calculate the number of possible arrangements of a set of objects with replacement. In this tutorial, we will show you how to use the Permutation with Replacement Calculator to calculate the number of possible arrangements of a set of objects.

 Set/Population Subset/Sample
 PR(n,r)

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## What is Permutation with Replacement?

Permutation with replacement is a concept in combinatorics that refers to the number of possible arrangements of a set of objects where each object can be used more than once. Permutation with replacement is commonly used in probability theory, as well as in the study of permutations and combinations in mathematics.

## The Formula for Permutation with Replacement

The formula for permutation with replacement is:

### Permutation with Replacement Formula

nr

Where n is the number of objects in the set, and r is the number of objects to be arranged.

## Example Calculation

Let's say that you have a set of three colors: red, green, and blue. You want to arrange these colors in groups of two, with replacement. To calculate the number of possible arrangements, you would use the following formula:

Number of Possible Arrangements = 32 = 9

This means that there are nine possible ways to arrange two colors from the set of three colors, with replacement. These possible arrangements are:

• Red-Red
• Red-Green
• Red-Blue
• Green-Red
• Green-Green
• Green-Blue
• Blue-Red
• Blue-Green
• Blue-Blue

## Conclusion

The Permutation with Replacement Calculator is a useful tool for calculating the number of possible arrangements of a set of objects with replacement. It can be used in a variety of applications, such as in probability theory or in the study of permutations and combinations in mathematics. By following the formula outlined in this tutorial, you can quickly and easily calculate the number of possible arrangements and make informed decisions based on your calculations.

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