# List permutations with repetition and how many to choose from

This article demonstrates a macro that lets you create a list of permutations, repetitions are allowed, based on a number of comma-delimited strings and the number of items per row.

The image above shows a list created by the macro based on numbers 1, 2, and 3 and five items per row.

### What's on this page

Noel asks:

Is there a way where I can predict all possible outcomes in Excel in the below example?

Total games are 13 (ABCDEFGHIJKLM). Possible outcomes are win(home team), draw or win(Away team) represented by 1, X or 2 respectively. Outcomes should be in the below formats:

111111111111X

11111111111XX

2222222X22221

222222222222X

## 2. VBA code

The following macro lets you enter text strings separated by a comma and the number of games.

Sub ListPermut() 'This macro creates a list of all permutations 'Get digital Help - https://www.get-digital-help.com/ 'Define variables Dim ws As Worksheet, Ans As String, ans1() As String, digits As Integer Dim num As Integer, p As Long, i As Long, t As Long Dim rng() As Long, c As Long, rng1() As String 'Insert a new sheet Set ws = Sheets.Add 'Ask for user input Ans = InputBox("Type strings separated with a comma:") digits = InputBox("How many strings?") 'Split text strings to an array ans1 = Split(Ans, ",") 'Count values in aray num = UBound(ans1) + 1 'Calculate number of permutations p = num ^ digits 'Redimension arrays ReDim rng(1 To digits) ReDim rng1(1 To digits) 'Save 1 to all values in first row of array For c = 1 To digits rng(c) = 1 Next c i = 0 'Don't show the result until finished Application.ScreenUpdating = False 'Repeat until all permutations have been created Do Until (i + t) = (p - 1) 'Use text strings instead of numbers For c = LBound(rng1) To UBound(rng1) rng1(c) = ans1(rng(c) - 1) Next c 'Transfer values from array to worksheet ws.Range("A1").Resize(, digits).Offset(i) = rng1 'Build next row of permutations For c = digits To 1 Step -1 If c = digits Then rng(c) = rng(c) + 1 ElseIf rng(c) = 0 Then rng(c) = rng(c - 1) End If If rng(c) = num + 1 Then rng(c) = 1 rng(c - 1) = rng(c - 1) + 1 End If Next c 'Count made permutations i = i + 1 'Insert a new sheet if rows exceed 999 999 If i = 1000000 Then Set ws = Sheets.Add t = t + 1000000 i = 0 End If Loop 'Use text strings instead of numbers For c = LBound(rng1) To UBound(rng1) rng1(c) = ans1(rng(c) - 1) Next c 'Transfer values from array to worksheet ws.Range("A1").Resize(, digits).Offset(i) = rng1 'Show output Application.ScreenUpdating = True End Sub

## 3. Where to copy code?

- Press Alt-F11 to open visual basic editor
- Press with left mouse button on Module on the Insert menu
- Copy and paste code above to the code module

- Exit visual basic editor (Alt+Q)

## 4. How to run the macro?

- Press Alt+F8 to open the macro dialog box
- Press with left mouse button on ListPermut macro
- Press with left mouse button on Run.

## 5. How to use the macro?

Enter your text stringsÂ using a comma as a text delimiting character.

Press with left mouse button on OK button.

Enter number of games.

Press with left mouse button on OK button.

Excel processes the data for a while and then createsÂ two sheets with a total ofÂ 1594323 permutations.

The picture shows 14 out ofÂ 1594323 permutations.

## 6. List permutations with repetition and how many to choose from (Excel 365 formula)

The Excel 365 formula in cell C3 spills to other adjacent cells automatically based on the values in the Excel Table (cell range I3:I5) and the number entered in cell K3.

You can add and delete strings in cell range I3:I5, the only limit is the worksheet row limit of 1 048 576. For example, 3 strings and 13 items return 1 594 323 rows and won't fit a worksheet.

You have to move the Excel Table and the value in cell K3 if you have more than 6 items, the Excel 365 formula returns a #SPILL! error if adjacent cells are populated.

Excel 365 dynamic array formula in cell C3:

Excel 365 formula in cell B3:

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### 4 Responses to “List permutations with repetition and how many to choose from”

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I have 17 games to bet, and am suppose to choose win, loose and draw.

How can I create a table with 17,matches with win,lose and draw? How many table will appear?

jimmy munisi,

The outcome is either win, lose or draw, three possibilities.

There are 17 games. 3^17 = 129 140 163 permutations.

If you want to list all permutations in a workbook, each sheet has 1 048 576 rows.

129 140 163 / 1 048 576 = 123.1 sheets

You need 124 worksheets in a workbook to list all permutations.

Hi, if I create a table with more than 10 elements, I get an error in all the cells that should contain an element >10. I would like to know how I could resolve. Thanks!

=INDEX(Table1[Strings], MID(BASE(SEQUENCE(PERMUTATIONA(COUNTA(Table1[Strings]),$K$3))-1, COUNTA(Table1[Strings]), $K$3), SEQUENCE(, $K$3), 1)+1) Using this formula. Sorry I forgot to specify.