How many permutations are in the word?

The below are some of example queries to which users can find how many ways to arrange letters in a word by using this word permutation or letters arrangement calculator:

Just give a try the words such as HI, FOX, ICE, LOVE, KIND, PEACE, KISS, MISS, JOY, LAUGH, LAKES, MATH, STATISTICS, MATHEMATICS, COEFFICIENT, PHONE, COMPUTER, CORPORATION, YELLOW, READ and WRITE to know how many ways are there to order the 2, 3, 4, 5, 6, 7, 8, 9 or 10 letters word. Users also supply any single word such as name of country, place, person, animal, bird, ocean, river, celebrity, scientist etc. to check how many ways the alphabets of a given word can be arranged by using this letters arrangement or permutation calculator.

Below is the reference table to know how many different ways to arrange 2, 3, 4, 5, 6, 7, 8, 9 or 10 letters word can be arranged, where the order of arrangement is important. The n-factorial (n!) is the total number of possible ways to arrange a n-distinct letters word or words having n-letters with some repeated letters. Refer permutation formula to know how to find nPr for different scenarios such as:

1. finding word permutation for words having distinct letters,
2. finding word permutation for words having repeated letters.

Work with Steps: How many Distinct Ways to Arrange the Letters of given Word

Supply the word of your preference and hit on FIND button provides the answer along with the complete work with steps to show what are all the parameters and how such parameters and values are being used in the permutation formula to find how many ways are there to order the letters in a given word. Click on the below words and know how the calculation is getting changed based on the word having distinct letters and words having repeated letters. For other words, use this letters of word permutations calculator.

Note: Permutation is a one-to-one mapping from a finite set to itself or an ordering of a finite set of distinct elements. In other words, permutation is a transformation of a set’s prime form, by applying one or more of certain operations, specifically, transposition, inversion and retrograde.

Instead of generating every permutation and filtering the duplicates, it's also possible to generate the list directly without any duplicate. Here's an example.

It generates $\frac{10!}{9!}$ ($=10$) strings without having to generate $10!$ strings and removing $10*(9!-1)$ duplicates:

Since all letters are unique, we have 7 options for what letter goes first, then the remaining 6 options for what's 2nd, etc.

The total number of permutations is the product of how many options there are for each position:

#7! = 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1 = 5040#

If some letters are duplicated, we would divide by the number of ways to permute those duplications, after permuting all the letters.

Example: How many ways can the letters of BANANA be permuted?

We have 1 B, 3 A's and 2 N's. So the number of permutations for BANANA are:

#(6!)/(1!xx3!xx2!)=60#

(Notice how the 6 on top equals the sum of the 1, 3, 2 on bottom. This is technically what we did for the letters in NUMBERS above, but since all letters were unique, we did

Above are the words made by unscrambling A R R A N G E (AAEGNRR). Our unscramble word finder was able to unscramble these letters using various methods to generate 84 words! Having a unscramble tool like ours under your belt will help you in ALL word scramble games!

How many words can you make out of ARRANGE?

To further help you, here are a few word lists related to the letters ARRANGE

A R R A N G E Letter Values in Word Scrabble and Words With Friends

Here are the values for the letters A R R A N G E in two of the most popular word scramble games.

Scrabble

The letters ARRANGE are worth 8 points in Scrabble

Words With Friends

The letters ARRANGE are worth 10 points in Words With Friends

If You Unscramble ARRANGE... What Does It Mean?

Definition of ARRANGE When Unscrambled

If we unscramble these letters, ARRANGE, it and makes several words. Here is one of the definitions for a word that uses all the unscrambled letters:

To calculate the amount of permutations of a word, this is as simple as evaluating#n!#, where n is the amount of letters. A 6-letter word has#6! =6*5*4*3*2*1=720#different permutations.

To write out all the permutations is usually either very difficult, or a very long task. As you can tell, 720 different "words" will take a long time to write out. There are computer algorithms and programs to help you with this, and this is probably the best solution.

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