 # Generating subsets of k elements out of a set of n elements

In Excel, how do you do generate, for example all subsets of 3 elements out of a set of 10 elements.

# Re: Generating subsets of k elements out of a set of n elements

Here is some VBA code adapted from Return all combinations

``````'Dimension public variable and declare data type
Public result() As Variant

'Name User Defined Function
Function Combinations(rng As Range, n As Single)
Dim rng1
'Save values from cell range rng to array variable rng1
rng1 = rng.Value
'Redimension array variable result
ReDim result(n - 1, 0)
'Start User Defined Function Recursive with paramters rng1, n, 1, 0
Call Recursive(rng1, n, 1, 0)
'Remove a column of values from array variable result
ReDim Preserve result(UBound(result, 1), UBound(result, 2) - 1)
'Transpose values in variable result and then return result to User Defined Function on worksheet
Combinations = Application.Transpose(result)
End Function

'Name User Defined Function and paramters
Function Recursive(r As Variant, c As Single, d As Single, e As Single)
'Dimension variables and declare data types
Dim f As Long, g As Long
'For ... Next statement
For f = d To UBound(r, 1)
'Save value in array variable r row f column 1 to array variable result row e and last column
result(e, UBound(result, 2)) = r(f, 1)
'If ... Then ... Else ... End If statement
'Check if variable in e is equal to c -1
If e = (c - 1) Then
'Add another column to array variable result
ReDim Preserve result(UBound(result, 1), UBound(result, 2) + 1)
'For ... Next statement
For g = 0 To UBound(result, 1)
'Save value in array variable result row g second last column to result row g last column
result(g, UBound(result, 2)) = result(g, UBound(result, 2) - 1)
Next g
'Continue here if e is not equal to c - 1
Else
'Start User Defined Function Recursive with parameters r, c, f + 1, e + 1
Call Recursive(r, c, f + 1, e + 1)
End If
Next f
End Function``````

Use like this:

Enter the elements in a range, for example A1:A10.

Select a range large enough for the output (in Excel in Microsoft 365 you only need to select the top left cell).

Enter the formula =Combinations(A1:A10,3)

If you're not on Microsoft 365, confirm the formula with Ctrl+Shift+Enter.