Creating Permutations in Excel

Creating permutations in Excel involves generating all possible arrangements of a set of items. While Excel doesn’t have a built-in permutation function, you can achieve this by using formulas and techniques.

Here’s a step-by-step guide on how to create permutations in Excel:

Step 1: Prepare Your Data

Begin by listing the items for which you want to generate permutations in a column. For example, you can have your items in column A from cell A1 to An.

Step 2: Create a Helper Column

In an adjacent column (e.g., column B), create a formula to help generate permutations. In cell B1, enter the number 1. In cell B2, enter the formula:


Drag this formula down to cover the entire range of your items. It will create a series of numbers from 1 to n, where n is the number of items.

Step 3: Calculate Factorials

In another cell (e.g., cell C1), calculate the factorial of the number of items in your list. Use the formula:


For example, if you have 5 items, you’d use:


Step 4: Generate Permutations

In an adjacent column (e.g., column D), use formulas to generate permutations. In cell D1, enter the following formula:


Replace “A$1:A$5” with the range of your items, and “B1” with the number from your helper column. Drag this formula down to cover the entire range of your items. Column D will now contain all the permutations of your items.

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Step 5: Review the Permutations

Column D contains all the permutations of your items. If you want to retain the permutations without the formulas, copy the values and paste them as values (right-click, Paste Special, Values).

Please note that for large sets of items, generating permutations can be computationally intensive, and alternative methods or specialized software may be necessary.