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. For instance, if you put 26 letters (A through Z) in cell A1 and the value 5 in cell A2, the macro will crash if you aren't using Excel 2007. Why? Because there are 65,780 possible five-character combinations and only 65,536 rows in which to place them.