**Please Note: **
This article is written for users of the following Microsoft Excel versions: 2007, 2010, and 2013. If you are using an earlier version (Excel 2003 or earlier), *this tip may not work for you*. For a version of this tip written specifically for earlier versions of Excel, click here: Listing Combinations.

Ron knows he can use the COMBIN function to determine the number of combinations that can be made from a number of digits. He's wondering, however, if there is a way to list out all the combinations themselves.

There is no built-in way to list combinations in Excel. You can, however, create a macro to do the listing for you. If you want to find the unique combinations in a set of sequential numbers starting at 1, then the following set of macros will do the trick. All you need to do is run the function TestCNR and you will end up with a "matrix" of cells that represent the number of 4-digit combinations in the sequential set of values ranging from 1 to 10.

Sub TestCNR() Cnr 10, 4 End Sub

Sub Cnr(n, r) i = 1 For j = 1 To r Cells(i, j).Value = j Next Do Until Finished(n, r, i) j = FindFirstSmall(n, r, i) For k = 1 To j – 1 Cells(i + 1, k).Value = Cells(i, k).Value Next Cells(i + 1, j).Value = Cells(i, j).Value + 1 For k = j + 1 To r Cells(i + 1, k).Value = Cells(i + 1, k - 1).Value + 1 Next i = i + 1 Loop End Sub

Function Finished(n, r, i) Temp = True For j = r To 1 Step -1 If Cells(i, j).Value <> j + (n - r) Then Temp = False End If Next Finished = Temp End Function Function FindFirstSmall(n, r, i) j = r Do Until Cells(i, j).Value <> j + (n - r) j = j - 1 Loop FindFirstSmall = j End Function

The macro overwrites whatever is in your worksheet, so make sure you run the test with a blank worksheet displayed. If you want to change the size of the set or the number of elements in the subset, just change the values passed in the TestCNR routine.

If you want to pull unique combinations from a string of characters (for instance, the letters of the alphabet), then you need to use a different set of macros. The following will work fine; it assumes that the characters you want to use as your "universe" is in cell A1 and the number you want in each unique combination is in cell A2.

Sub FindSets() Dim iA() As Integer Dim sUniv As String Dim iWanted As Integer Dim j As Integer Dim k As Integer sUniv = Cells(1, 1).Value iWanted = Cells(2, 1).Value ReDim iA(iWanted) For j = 1 To iWanted iA(j) = j Next j iRow = PutRow(iA, sUniv, 1) Do Until DoneYet(iA, Len(sUniv)) j = WorkHere(iA, Len(sUniv)) iA(j) = iA(j) + 1 For k = j + 1 To iWanted iA(k) = iA(k - 1) + 1 Next k iRow = PutRow(iA, sUniv, iRow) Loop End Sub

Function DoneYet(iB, n) As Boolean iMax = UBound(iB) Temp = True For j = iMax To 1 Step -1 If iB(j) <> j + (n - iMax) Then Temp = False End If Next DoneYet = Temp End Function

Function WorkHere(iB, n) As Integer iMax = UBound(iB) j = iMax Do Until iB(j) <> j + (n - iMax) j = j - 1 Loop WorkHere = j End Function

Function PutRow(iB, sUniv, i) iMax = UBound(iB) sTemp = "" For j = 1 To iMax sTemp = sTemp & Mid(sUniv, iB(j), 1) Next j Cells(i, 2).Value = sTemp PutRow = i + 1 End Function

Run the FindSets macro and the different combinations desired end up in column 2. Be careful when running the macro, however. The number of combinations can get very large very quickly.

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This tip (11891) applies to Microsoft Excel 2007, 2010, and 2013. You can find a version of this tip for the older menu interface of Excel here: **Listing Combinations**.

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2018-02-16 21:51:46

Ken Kast

Also there is a typo (extra line) Set c=c that should be removed.

2018-02-14 16:22:14

Ken Kast

Sub xCnr(n As Integer, r As Integer, T As Variant, c As Range)

Dim j As Integer

If n > 0 And r > 0 Then

If r = 1 Then

Set c = c

For j = n To 1 Step -1

T(1) = j

c.Value = T

Set c = c.Offset(1, 0)

Next j

Else

For j = n To 1 Step -1

T(r) = j

Call xCnr(j - 1, r - 1, T, c)

Next j

End If

End If

End Sub

Sub TestxCnr()

Dim T As Variant

Dim length As Integer

length = 4

ReDim T(1 To length) As Variant

xCnr 10, length, T, ActiveSheet.Cells(1, 1).Resize(1, UBound(T))

End Sub

2017-01-18 10:18:13

greg

Actually, the method is quite brilliant. I went through the code step by step and its great

2016-02-10 07:55:17

allen@sharonparq.com

Fred: You can sign up using the form at the right side of this page or any page on this site.

-Allen

2016-02-09 22:25:47

Fred Mirande

I have been a long time subscriber to daily tips Excel 2007.

Laptop died some months back after retirement. Did not think I would get another, but, I did and now realise that I miss your tips. Please can I subscribe with my new email address. I was lmirande@bigpond but is not now. Thanks, Kind Regards Fred Mirande9

2015-01-04 00:09:49

Steve

2014-04-25 21:44:57

Zefs

I have been mucking around for a while.

Could you add the changes in the Macro below as I have been unsuccessful. I would like the Combination Generator to continue to sheet 2 & 3 & 4... if needed etc, etc if it exceeds the sheet limit of 1048575. Also to numer the combinations starting in column A and continuing to the following sheets.

Regards, Zefs.

Sub TestCNR()

Cnr 10, 4

End Sub

Sub Cnr(n, r)

i = 1

For j = 1 To r

Cells(i, j).Value = j

Next

Do Until Finished(n, r, i)

j = FindFirstSmall(n, r, i)

For k = 1 To j – 1

Cells(i + 1, k).Value = Cells(i, k).Value

Next

Cells(i + 1, j).Value = Cells(i, j).Value + 1

For k = j + 1 To r

Cells(i + 1, k).Value = Cells(i + 1, k - 1).Value + 1

Next

i = i + 1

Loop

End Sub

Function Finished(n, r, i)

Temp = True

For j = r To 1 Step -1

If Cells(i, j).Value <> j + (n - r) Then

Temp = False

End If

Next

Finished = Temp

End Function

Function FindFirstSmall(n, r, i)

j = r

Do Until Cells(i, j).Value <> j + (n - r)

j = j - 1

Loop

FindFirstSmall = j

End Function

2014-04-08 04:28:12

Zefs

Thanks so much for the reply.

I see you commented on the second Macro. For some reason I couldn't get that working. I am using the first Macro and it is quite different. Do you mind having a look at what the solution would be for that Macro. Sorry, but a newbie.

Regards,

Zefs,

Tasmania.

2014-04-07 11:17:33

Michael (Micky) Avidan

You need to make some minor changes.

In the the main macro put a variable LC, give it the value of 2 (LC = 2) and send fourth variable, to the "PutRow" Function.

This variable will serve for the column number.

So, insted of: Cells(i, 2).Value = sTemp

Use: Cells(i, LC).Value = sTemp

All you need, now, is to check/find out when does the row counter (i) reaches: 1048575 and if so, increase the LC by 1 (LC = LC +1) in order to put the next value in row 1 of the next(!) column.

All the above are general instructions given from a short look at the proposed macros (I didn't check this out).

Michael (Micky) Avidan

“Microsoft® Answers" - Wiki author & Forums Moderator

“Microsoft®” MVP – Excel (2009-2014)

ISRAEL

2014-04-06 10:59:16

Zefs

Problem I have been having for a while is my exc2007 only has a limit up to approx 1.04million rows. When the combinations reach this target, the macro stops producing combinations. Is there any way to extend the rows in the page, be it via an after market add in or hacking excel somehow? If Not, can the Macro continue producing the combinations to a new page tab. If so, what is important to me is that the row number of the combination continues to the next page rather than starting from 1 again. If the row number cannot continue, can the macro be enabled to have the combination number in row A and continue to the next pages?

Regards, Zefs.

2013-10-15 13:31:18

Bryan

1. All variables should be dimensioned. If you have the "Require Variable Declaration" option checked (aka Option Explicit), as you should, the macros won't compile. It also makes it easier to tell what the variables are supposed to be.

2. Function inputs and outputs should have a declared type, not an implicit Variant type.

3. The i/j/k variables are fine (by convention, counter variables are often single letters starting with i), but the rest of the variables could be more clearly named.

4. Similarly, some of the functions are cryptically named. "CNR" means... COMBIN n r? Why not ListCombinations? "Finished" and "DoneYet" are more or less clear enough, "FindFirstSmall" and "PutRow" are mediocre, and "WorkHere" is just downright useless.

5. Since Finished and DoneYet don't need to continue looping once Temp = False, you should add an Exit For condition so you aren't needlessly looping.

6. With all the loops and subroutines, a couple comments would go a long way to explaining what is going on. Something as simple as "' This routine determines if we have reached the last combination" is all that is needed for "Finished", for example. Another comment on how the "last combination" is determined wouldn't hurt either.

7. Hard-coding an output range without any sort of check is a Very Bad Idea. At a minimum you should (a) prompt the user or somehow let the user choose an output range (by using the Selection object, for example; one of the few good uses of this object); (b) check how many rows will be occupied to determine if you will have enough room (choosing 8 letters from the alphabet gives >1.5m combinations; too great to fit within the sheet) and that there's nothing currently occupying the space; and (c) clear the space needed and possibly the surrounding area (cnr 10, 4 followed by cnr 5, 4 will give the appearance of an incorrect result).

8. Application.ScreenUpdating = False will drastically speed up large number of combinations; using a variant array and putting it all back to the sheet at once will increase the speed even more

9. I'm sure there are more, but as I mentioned I just can't follow the code well enough to suggest any substantial changes.

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