# Permutation with Repetition Calculator

Our permutation with repetition calculator will help you determine the different ways you can **order** your objects. You can also use this calculator to *list all permutations* possible with your set of objects. In this article, we shall:

- Define permutation.
- Learn the formula for permutation with repetition.
- Look at an example permutation calculation.

## What are permutations?

Say you have to set a new 4-digit pin for your device. You can arrange the ten numbers from 0 to 9 into these four places in any order. Each possible arrangement is called a * permutation*.

*Permutation is an arrangement of items in a particular order from a given set of items.*

**Permutation with repetition**: When *items* in the set are *repeated* in the arrangement, it is a permutation with repetition. In the above example, pins like `3242`

or `4555`

have repeated items (`2`

and `5`

).

**Permutation without repetition**: When *duplication of items* is *not allowed* in the arrangement, it is a permutation without repetition. Each item in the permutation is unique. In such cases, pins like `3242`

are not allowed since `2`

occurs twice. However, `4321`

is allowed since each digit is unique.

## Permutation with repetition formula

The formula for permutation with repetition is:

where:

- $n$ – Number of items in the set;
- $P$ – Total number of possible permutations; and
- $r$ – Number of items allowed in each permutation.

Read $^nP_r$ as the number of ways to arrange $n$ items in $r$ places. Note that other representations such as $P^n_r$ and $P(n,r)$ are also common.

## How do you calculate permutation with repetition?

To calculate the number of permutations with repetition when arranging *n* items in *r* places, simply multiply *n* with itself *r* times. * ⁿPᵣ = nʳ*.

Going back to our four-digit pin problem, let's work out how many permutations are possible with repetition using the permutation equation:

You have 10,000 possible permutations to choose from, so take the opportunity to set a hard-to-guess pin and keep your data safe from prying fingers! Avoid easy-to-guess pins like your birth year or 1234.

## How to use this permutation with repetition calculator

Omni strives to make our tools versatile and robust while keeping things user-friendly. You'll find that our permutation with repetition calculator is no exception to this rule:

- Enter the total number of objects
`n`

and the sample size`r`

. - The calculator will automatically give you:
- Permutations with repetition; and
- Permutations without repetition, so you can compare the two.

- This calculator will also
if the total number doesn't exceed the maximum display preset of**list all possible permutations****2000**. You can change this value in the`advanced mode`

, but a lengthier list may not be convenient.

## Other relevant calculators

We have more calculators related to permutations and combinations for you:

## FAQ

### How many different 10-character passwords are possible using only alpha numerals?

There are **839,299,365,868,340,224** possible permutations. You can calculate this yourself by approaching this as a *permutation with repetition* problem:

- Determine the
**total number of items**available for permutation:- Accounting for upper and lower case English alphabets gives 52 characters.
- There are ten digits from 0 to 9. Hence we have 62 characters in total.

- Calculate the number of ways we can arrange 62 characters into 10 places when repetition is allowed:
**62¹⁰ = 839,299,365,868,340,224**.