Permutation is such a great mathematical concept that has a significant impact on every aspect of education. We can see its usage in math, quantum physics, computer science, etc. In this article, we’ll demonstrate how we can calculate permutations in ** 3** different methods without repetition in Excel. So, let’s go through the article entirely to grab a good dexterity on it.

## Download Practice Workbook

You may download the following Excel workbook for better understanding and practice yourself.

## Basics of Permutation

The permutation is a computational method that establishes the total number of alternative configurations in a collection when the sequence of the arrangements matters. Picking only a few items from a collection of options in a specific sequence is a common task in arithmetic problems. Permutations are frequently confused with another mathematical concept, combination. The sequence in which the components are selected does not, however, affect combinations. In other words, whereas “ab” and “ba” are equal in combinations, they are deemed to be different arrangements in permutations. Let’s see an example to understand it better.

Let’s say you have ** three** letters:

**,**

*A***, and**

*B***. Suppose we tell you to make different words containing**

*C***letters with these letters. So, you could construct**

*two***,**

*AB***,**

*BA***,**

*BC***,**

*CB***, and**

*AC***. Hence, there would be**

*CA***different 2-letter words created from these**

*6***letters. Therefore, here,**

*3***is the total number of objects in the set. We can express it with the letter**

*3***n**. And

**is the specific number of chosen objects that can be substituted for k. So, the general formula for permutation is the following.**

*2*

^{n}P_{k}= n! / (n-k)!## 3 Methods to Calculate Permutations Without Repetition in Excel

For ease of understanding, we are going to use a ** List of Numbers and Groups**. This dataset contains the

**and**

*Numbers***under columns**

*Chosen Group***B**and

**C**respectively.

Now, we’ll use this dataset to calculate permutations using ** 3** various methods without repetition in Excel. So, let’s explore them one by one.

Here, we have used the

*Microsoft Excel 365*version, you may use any other version according to your convenience.

### 1. Using PERMUT Function

In our first method, we’ll get help from the **PERMUT function**. It returns the number of permutations without repetition for a certain number of items that can be chosen from a number of objects. So, let’s see the steps below to do it our way.

**📌**** Steps:**

- At the very beginning, create a new column with the heading called
under*Permutations***Column D**.

- Then, select cell
**D5**and enter the following formula into that cell.

`=PERMUT(B5,C5)`

Here, **B5** and **C5** represent the first ** Number** and the first

**correspondingly.**

*Chosen Group*- After that, press the
**ENTER**key.

- At this time, bring the cursor to the right-bottom corner of cell
**D5**and it will look like a plus**(+)**sign. Actually, it’s the**Fill Handle**tool. - Following this, double-click on it.

Instantly, it’ll copy the formula to the lower cells and give us output in the remaining cells also.

### 2. Utilizing FACT Function

In this section, we’ll follow the manual process to calculate permutations in Excel. To do this, we’ll insert the **FACT function**. It’s simple and easy; just follow along.

**📌**** Steps:**

- First, go to cell
**D5**and insert the formula below.

`=FACT(B5)/FACT(B5-C5)`

- Then, press
**ENTER**.

That’s how we can easily find the permutations for defined numbers and groups.

### 3. Applying Combined Formula

In our last method, we’ll employ multiple functions to achieve our goals. So, without further delay, let’s dive in!

**📌**** Steps:**

- Firstly, select cell
**C5**and paste the following formula.

`=SUM(IF(LEN(B5)-LEN(SUBSTITUTE(UPPER(B5),CHAR(ROW(INDIRECT("1:255"))),"")),1,0))`

**Formula Breakdown**

**ROW(INDIRECT(“1:255”))**→ Here the**ROW**and**INDIRECT**functions return the numbersto*1*in 255 different cells in a vertical array.*255***CHAR(ROW(INDIRECT(“1:255”))) →**the**CHAR function**returns a character based on the number given as an argument. Like, for, it returns an*33***Exclamation mark (!)**called**Factorial**.**UPPER(B5) →**the**UPPER function**converts the text to uppercase letters.- Output
**→ AABCF.**

- Output
**SUBSTITUTE(UPPER(B5),CHAR(ROW(INDIRECT(“1:255″))),””) →**the**SUBSTITUTE function**gets the output of**UPPER(B5)**as theargument. Then, it takes the output of*text***CHAR(ROW(INDIRECT(“1:255”))**as theargument and a blank space as the*old_text*argument.*new_text***LEN(SUBSTITUTE(UPPER(B5),CHAR(ROW(INDIRECT(“1:255″))),””)) →**the**LEN function**returns the length of the text strings in the vertical array.**IF(LEN(B5)-LEN(SUBSTITUTE(UPPER(B5),CHAR(ROW(INDIRECT(“1:255″))),””)),1,0) →**the**IF function**implies a logical test. If the result of the subtraction becomes greater than zero, then it returns, otherwise, it’ll return*1*.*0***SUM(IF(LEN(B5)-LEN(SUBSTITUTE(UPPER(B5),CHAR(ROW(INDIRECT(“1:255″))),””)),1,0)) →**the**SUM function**totals all the output in the array and returns the output in cell**C5**.- Output
**→ 4**

- Output

- Then, tap the
**ENTER**key.

Now, we have extracted the number of unique letters in each text string. Therefore, we can easily calculate the number of permutations for each row. For example, we took the group of ** 2** letters for the first example.

- So, go to cell
**E5**and write down the following formula.

`=PERMUT(C5,D5)`

- As always, press
**ENTER**.

You can use this formula for text strings of various lengths as you wish.

## Practice Section

For doing practice by yourself, we have provided a **Practice** section like the one below on each sheet on the right side. Please do it yourself.

## Conclusion

This article explains how to calculate permutations without repetitions in Excel in a simple and concise manner. Don’t forget to download the **Practice** file. Thank you for reading this article. We hope this was helpful. Please let us know in the comment section if you have any queries or suggestions. Please visit our website, **Exceldemy**, a one-stop Excel solution provider, to explore more.