This program uses a recursive subroutine that first checks combinations containing the first allowed value, and then considers combinations that do not contain the first allowed value.
This is a modified tree search. It looks in all possible combinations of items to find those that have exactly N items selected.
For more information on tree searching and other algorithms (albeit in Visual Basic 6), see my book ReadytoRun Visual Basic Algorithms, Second Edition.

' Pick N items from a list between first_allowed
' and last_allowed. Return the solutions in the
' collection as spaceseparated characters.
'
' For example, MchoseN(3, 2, 5, solutions) means
' pick 3 items from the values 2, 3, 4, 5 and
' returns 2 3 4, 2 3 5, and 3 4 5.
Private Sub MchoseN(ByVal N As Integer, ByVal first_allowed _
As Integer, ByVal last_allowed As Integer, ByVal _
solutions As Collection)
' If N < 1, we don't need to pick any more
' items.
' If N > last_allowed  first_allowed + 1,
' there are too few items for a solution.
' If N = last_allowed  first_allowed + 1,
' all the items must be in the solution.
If N < 1 Then
' We don't need to pick any more.
' Do nothing.
ElseIf N > last_allowed  first_allowed + 1 Then
' There are not enough items.
' Do nothing.
ElseIf N = last_allowed  first_allowed + 1 Then
' All the items must be in the solution.
Dim txt As String = Format$(first_allowed)
For i As Integer = first_allowed + 1 To last_allowed
txt = txt & " " & Format$(i)
Next i
solutions.Add(txt)
Else
' Get solutions containing first_allowed.
Dim partial_solutions As New Collection()
If N = 1 Then
partial_solutions.Add("")
Else
MchoseN(N  1, first_allowed + 1, last_allowed, _
partial_solutions)
End If
' Add first_allowed to make the full
' solutions.
For i As Integer = 1 To partial_solutions.Count
solutions.Add(Format$(first_allowed) & _
" " & partial_solutions(i))
Next i
' Get solutions not containing first_allowed.
partial_solutions = New Collection()
MchoseN(N, first_allowed + 1, last_allowed, _
partial_solutions)
' Add these to the solutions.
For i As Integer = 1 To partial_solutions.Count
solutions.Add(partial_solutions(i))
Next i
End If
End Sub

Private Sub btnList_Click(ByVal sender As System.Object, _
ByVal e As System.EventArgs) Handles btnList.Click
' Get the solutions.
Dim solutions As New Collection()
Dim M As Integer = Val(txtM.Text)
Dim N As Integer = Val(txtN.Text)
MchoseN(N, 1, M, solutions)
' Display the solutions.
lstResults.Items.Clear()
For i As Integer = 1 To solutions.Count
lstResults.Items.Add(solutions(i))
Next i
txtSolutions.Text = Format$(solutions.Count)
' Calculate the number of combinations directly.
txtCalculatedNumber.Text = _
Factorial(M) / _
Factorial(N) / _
Factorial(M  N)
End Sub
