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I have a math question

Topic closed. 22 replies. Last post 11 months ago by dr san.

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Canada
Member #137795
January 12, 2013
24 Posts
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Posted: December 31, 2015, 2:34 pm - IP Logged

Pick 4,        1 to 38,      ? - ? - ? - ?,     = 73,815 combinations, is this correct ?

Yes.

 

Pick 4,        ?-?-?-?,    1 to 11 for first position,   5 to 24 for second position, 12 to 34 for third position, 19 to 37 for fourth position, = ? combinations.

is it 4006?

No.

 

it is 39,389

Hey, ya'll, Thanks for helping me out. I figured it out by cutting  and pasting with excel, took me 6 and a half hours, which is WHY I had to ask for help.

Looks like JADELottery had the correct answer to my question.    = 39,389,

later on when I am done with my little project, ill let you in on what i figured out and Ill ask for your opinions on my findings, Thanks again

.

    JADELottery's avatar - MeAtWork 03.PNG
    The Quantum Master
    West Concord, MN
    United States
    Member #21
    December 7, 2001
    3675 Posts
    Offline
    Posted: December 31, 2015, 3:22 pm - IP Logged

    Hey, ya'll, Thanks for helping me out. I figured it out by cutting  and pasting with excel, took me 6 and a half hours, which is WHY I had to ask for help.

    Looks like JADELottery had the correct answer to my question.    = 39,389,

    later on when I am done with my little project, ill let you in on what i figured out and Ill ask for your opinions on my findings, Thanks again

    .

    Thanks.

    Here's the Excel VB code we used to generate the combinations.

    ____________________________________________________________________________________________________

    Function Fact(ByVal n As Integer) As Double
        On Error GoTo exitfunction
        If (n <= 1) Then
            Fact = 1
        Else
            Fact = n * Fact(n - 1)
        End If
        Exit Function
    exitfunction:
        Fact = -1
    End Function

    Function Perm(ByVal n As Integer, ByVal R As Integer) As Double
        On Error GoTo exitfunction
        Dim a As Integer
        Dim b As Double
        b = 1
        If (n < R) Then
            Perm = 0
        Else
            For a = (n - (R - 1)) To n
                b = b * a
            Next a
            Perm = b
        End If
        Exit Function
    exitfunction:
        Perm = -1
    End Function

    Function Comb(ByVal n As Integer, ByVal R As Integer) As Double
        On Error GoTo exitfunction
        If (n < R) Then
            Comb = 0
        Else
            Comb = Perm(n, R) / Fact(R)
        End If
        Exit Function
    exitfunction:
        Comb = -1
    End Function

    Function Cdist(ByVal n As Integer, ByVal R As Integer, ByVal C As Integer, ByVal Z As Integer) As Double
        On Error GoTo exitfunction
        If ((Z < C) Or (Z > (n - (R - C))) Or (Z > n) Or (C > R) Or (n < 1) Or (R < 1) Or (C < 1) Or (Z < 1)) Then
            Cdist = 0
        Else
            Cdist = Comb((Z - 1), (C - 1)) * Comb((n - Z), (R - C))
        End If
        Exit Function
    exitfunction:
        Cdist = -1
    End Function

    Function fColumnSum(ByVal n As Integer, ByVal R As Integer, ByVal Z As Integer) As Double
        On Error GoTo exitfunction
        Dim a As Integer
        Dim ColumnSum As Double
        If (Z < 1) Then
            fColumnSum = 0
        ElseIf ((Z >= 1) And (Z < (n - (R - 1)))) Then
            ColumnSum = 0
            For a = 1 To Z
                ColumnSum = ColumnSum + Cdist(n, R, 1, a)
            Next a
            fColumnSum = ColumnSum
        ElseIf (Z >= (n - (R - 1))) Then
            fColumnSum = Comb(n, R)
        End If
        Exit Function
    exitfunction:
        fColumnSum = -1
    End Function

    Function Index2Combin(ByVal n As Integer, ByVal R As Integer, ByVal i As Double) As String
        On Error GoTo exitfunction
        Dim a, b, Combination(), Z As Integer
        Dim C, j As Double
        ReDim Combination(R)
        Dim tmpString, CombinFormat As String
        Dim NumberFound As Boolean
        tmpString = ""
        CombinFormat = ""
        C = Comb(n, R)
        j = i
        j = j - 1
        Z = 0
        b = Len(Format(n, "0"))
        For a = 1 To b
            CombinFormat = CombinFormat & "0"
        Next a
        For a = 1 To R
            If ((i >= 1) And (i <= C)) Then
                If (a = 1) Then
                    Combination(a) = 1
                Else
                    Combination(a) = Combination(a - 1) + 1
                End If
                NumberFound = False
                Do
                    Select Case (j - fColumnSum((n - Z), (R - (a - 1)), (Combination(a) - (Z + 1))))
                        Case Is < 0
                            Combination(a) = Combination(a) - 1
                            NumberFound = True
                        Case Is = 0
                            NumberFound = True
                        Case Is > 0
                            Combination(a) = Combination(a) + 1
                    End Select
                Loop Until NumberFound
                j = j - fColumnSum((n - Z), (R - (a - 1)), (Combination(a) - (Z + 1)))
                Z = Combination(a)
            Else
                Combination(a) = 0
            End If
            tmpString = tmpString & Format(Combination(a), CombinFormat)
            If (a < R) Then tmpString = tmpString & " "
        Next a
        Index2Combin = tmpString
        Exit Function
    exitfunction:
        Index2Combin = "err"
    End Function

    Function Combin2Index(ByVal n As Integer, ByVal R As Integer, ByVal theRange As Range) As Double
        On Error GoTo exitfunction
        Dim a As Integer
        Dim fSum As Double
        Dim NotInAscendingOrder, NotInPool As Boolean
        NotInAscendingOrder = False
        NotInPool = False
        If ((theRange.Rows.Count <> 1) Or (theRange.Columns.Count <> R)) Then
            Combin2Index = -1
            Exit Function
        End If
        For a = 1 To R
            If (a < R) Then
                If (theRange.Cells(1, a) >= theRange.Cells(1, (a + 1))) Then
                    NotInAscendingOrder = True
                End If
            End If
            If ((theRange.Cells(1, a) < 1) Or (theRange.Cells(1, a) > n)) Then
                NotInPool = True
            End If
        Next a
        If (NotInAscendingOrder Or NotInPool) Then
            Combin2Index = -1
            Exit Function
        End If
        fSum = 1
        For a = 1 To R
            If (a = 1) Then
                fSum = fSum + fColumnSum(n, R, (theRange.Cells(1, 1) - 1))
            Else
                fSum = fSum + fColumnSum((n - theRange.Cells(1, (a - 1))), (R - (a - 1)), (theRange.Cells(1, a) - (theRange.Cells(1, (a - 1)) + 1)))
            End If
        Next a
        Combin2Index = fSum
        Exit Function
    exitfunction:
        Combin2Index = -1
    End Function
    ____________________________________________________________________________________________________

    Presented 'AS IS' and for Entertainment Purposes Only.
    Any gain or loss is your responsibility.
    Use at your own risk.

    Order is a Subset of Chaos
    Knowledge is Beyond Belief
    Wisdom is Not Censored
    Douglas Paul Smallish
    Jehocifer

      SergeM's avatar - slow icon.png
      Economy class
      Belgium
      Member #123700
      February 27, 2012
      4035 Posts
      Offline
      Posted: December 31, 2015, 3:41 pm - IP Logged

      I think that ranges are just too easy.

      Do a mix such as:

      1 3 5 7 8
      6 7 8 9 10
      9 15 16 17 20
      30 34 38

      This pure mixing, not by indeces and you can leave out the rotten apples!

      I make this on LINK with groups:

      Input: [[1, 3, 5, 7, 8], [6, 7, 8, 9, 10], [9, 15, 16, 17, 20], [30, 34, 38]].

      Count of combinations: 315. Limit display: 3000.

      1 10 15 30
      1 10 15 34
      1 10 15 38
      1 10 16 30
      1 10 16 34
      1 10 16 38
      1 10 17 30
      1 10 17 34
      1 10 17 38
      1 10 20 30
      1 10 20 34
      1 10 20 38
      1 6 15 30
      1 6 15 34
      1 6 15 38
      1 6 16 30
      1 6 16 34
      1 6 16 38
      1 6 17 30
      1 6 17 34
      1 6 17 38
      1 6 20 30
      1 6 20 34
      1 6 20 38
      1 6 9 30
      1 6 9 34
      1 6 9 38
      1 7 15 30
      1 7 15 34
      1 7 15 38
      1 7 16 30
      1 7 16 34
      1 7 16 38
      1 7 17 30
      1 7 17 34
      1 7 17 38
      1 7 20 30
      1 7 20 34
      1 7 20 38
      1 7 9 30
      1 7 9 34
      1 7 9 38
      1 8 15 30
      1 8 15 34
      1 8 15 38
      1 8 16 30
      1 8 16 34
      1 8 16 38
      1 8 17 30
      1 8 17 34
      1 8 17 38
      1 8 20 30
      1 8 20 34
      1 8 20 38
      1 8 9 30
      1 8 9 34
      1 8 9 38
      1 9 10 30
      1 9 10 34
      1 9 10 38
      1 9 15 30
      1 9 15 34
      1 9 15 38
      1 9 16 30
      1 9 16 34
      1 9 16 38
      1 9 17 30
      1 9 17 34
      1 9 17 38
      1 9 20 30
      1 9 20 34
      1 9 20 38
      3 10 15 30
      3 10 15 34
      3 10 15 38
      3 10 16 30
      3 10 16 34
      3 10 16 38
      3 10 17 30
      3 10 17 34
      3 10 17 38
      3 10 20 30
      3 10 20 34
      3 10 20 38
      3 6 15 30
      3 6 15 34
      3 6 15 38
      3 6 16 30
      3 6 16 34
      3 6 16 38
      3 6 17 30
      3 6 17 34
      3 6 17 38
      3 6 20 30
      3 6 20 34
      3 6 20 38
      3 6 9 30
      3 6 9 34
      3 6 9 38
      3 7 15 30
      3 7 15 34
      3 7 15 38
      3 7 16 30
      3 7 16 34
      3 7 16 38
      3 7 17 30
      3 7 17 34
      3 7 17 38
      3 7 20 30
      3 7 20 34
      3 7 20 38
      3 7 9 30
      3 7 9 34
      3 7 9 38
      3 8 15 30
      3 8 15 34
      3 8 15 38
      3 8 16 30
      3 8 16 34
      3 8 16 38
      3 8 17 30
      3 8 17 34
      3 8 17 38
      3 8 20 30
      3 8 20 34
      3 8 20 38
      3 8 9 30
      3 8 9 34
      3 8 9 38
      3 9 10 30
      3 9 10 34
      3 9 10 38
      3 9 15 30
      3 9 15 34
      3 9 15 38
      3 9 16 30
      3 9 16 34
      3 9 16 38
      3 9 17 30
      3 9 17 34
      3 9 17 38
      3 9 20 30
      3 9 20 34
      3 9 20 38
      5 10 15 30
      5 10 15 34
      5 10 15 38
      5 10 16 30
      5 10 16 34
      5 10 16 38
      5 10 17 30
      5 10 17 34
      5 10 17 38
      5 10 20 30
      5 10 20 34
      5 10 20 38
      5 6 15 30
      5 6 15 34
      5 6 15 38
      5 6 16 30
      5 6 16 34
      5 6 16 38
      5 6 17 30
      5 6 17 34
      5 6 17 38
      5 6 20 30
      5 6 20 34
      5 6 20 38
      5 6 9 30
      5 6 9 34
      5 6 9 38
      5 7 15 30
      5 7 15 34
      5 7 15 38
      5 7 16 30
      5 7 16 34
      5 7 16 38
      5 7 17 30
      5 7 17 34
      5 7 17 38
      5 7 20 30
      5 7 20 34
      5 7 20 38
      5 7 9 30
      5 7 9 34
      5 7 9 38
      5 8 15 30
      5 8 15 34
      5 8 15 38
      5 8 16 30
      5 8 16 34
      5 8 16 38
      5 8 17 30
      5 8 17 34
      5 8 17 38
      5 8 20 30
      5 8 20 34
      5 8 20 38
      5 8 9 30
      5 8 9 34
      5 8 9 38
      5 9 10 30
      5 9 10 34
      5 9 10 38
      5 9 15 30
      5 9 15 34
      5 9 15 38
      5 9 16 30
      5 9 16 34
      5 9 16 38
      5 9 17 30
      5 9 17 34
      5 9 17 38
      5 9 20 30
      5 9 20 34
      5 9 20 38
      6 7 15 30
      6 7 15 34
      6 7 15 38
      6 7 16 30
      6 7 16 34
      6 7 16 38
      6 7 17 30
      6 7 17 34
      6 7 17 38
      6 7 20 30
      6 7 20 34
      6 7 20 38
      6 7 9 30
      6 7 9 34
      6 7 9 38
      6 8 15 30
      6 8 15 34
      6 8 15 38
      6 8 16 30
      6 8 16 34
      6 8 16 38
      6 8 17 30
      6 8 17 34
      6 8 17 38
      6 8 20 30
      6 8 20 34
      6 8 20 38
      6 8 9 30
      6 8 9 34
      6 8 9 38
      7 10 15 30
      7 10 15 34
      7 10 15 38
      7 10 16 30
      7 10 16 34
      7 10 16 38
      7 10 17 30
      7 10 17 34
      7 10 17 38
      7 10 20 30
      7 10 20 34
      7 10 20 38
      7 8 15 30
      7 8 15 34
      7 8 15 38
      7 8 16 30
      7 8 16 34
      7 8 16 38
      7 8 17 30
      7 8 17 34
      7 8 17 38
      7 8 20 30
      7 8 20 34
      7 8 20 38
      7 8 9 30
      7 8 9 34
      7 8 9 38
      7 9 10 30
      7 9 10 34
      7 9 10 38
      7 9 15 30
      7 9 15 34
      7 9 15 38
      7 9 16 30
      7 9 16 34
      7 9 16 38
      7 9 17 30
      7 9 17 34
      7 9 17 38
      7 9 20 30
      7 9 20 34
      7 9 20 38
      8 10 15 30
      8 10 15 34
      8 10 15 38
      8 10 16 30
      8 10 16 34
      8 10 16 38
      8 10 17 30
      8 10 17 34
      8 10 17 38
      8 10 20 30
      8 10 20 34
      8 10 20 38
      8 9 10 30
      8 9 10 34
      8 9 10 38
      8 9 15 30
      8 9 15 34
      8 9 15 38
      8 9 16 30
      8 9 16 34
      8 9 16 38
      8 9 17 30
      8 9 17 34
      8 9 17 38
      8 9 20 30
      8 9 20 34
      8 9 20 38

        Avatar
        New Member

        Canada
        Member #137795
        January 12, 2013
        24 Posts
        Offline
        Posted: December 31, 2015, 4:12 pm - IP Logged

        Thanks.

        Here's the Excel VB code we used to generate the combinations.

        ____________________________________________________________________________________________________

        Function Fact(ByVal n As Integer) As Double
            On Error GoTo exitfunction
            If (n <= 1) Then
                Fact = 1
            Else
                Fact = n * Fact(n - 1)
            End If
            Exit Function
        exitfunction:
            Fact = -1
        End Function

        Function Perm(ByVal n As Integer, ByVal R As Integer) As Double
            On Error GoTo exitfunction
            Dim a As Integer
            Dim b As Double
            b = 1
            If (n < R) Then
                Perm = 0
            Else
                For a = (n - (R - 1)) To n
                    b = b * a
                Next a
                Perm = b
            End If
            Exit Function
        exitfunction:
            Perm = -1
        End Function

        Function Comb(ByVal n As Integer, ByVal R As Integer) As Double
            On Error GoTo exitfunction
            If (n < R) Then
                Comb = 0
            Else
                Comb = Perm(n, R) / Fact(R)
            End If
            Exit Function
        exitfunction:
            Comb = -1
        End Function

        Function Cdist(ByVal n As Integer, ByVal R As Integer, ByVal C As Integer, ByVal Z As Integer) As Double
            On Error GoTo exitfunction
            If ((Z < C) Or (Z > (n - (R - C))) Or (Z > n) Or (C > R) Or (n < 1) Or (R < 1) Or (C < 1) Or (Z < 1)) Then
                Cdist = 0
            Else
                Cdist = Comb((Z - 1), (C - 1)) * Comb((n - Z), (R - C))
            End If
            Exit Function
        exitfunction:
            Cdist = -1
        End Function

        Function fColumnSum(ByVal n As Integer, ByVal R As Integer, ByVal Z As Integer) As Double
            On Error GoTo exitfunction
            Dim a As Integer
            Dim ColumnSum As Double
            If (Z < 1) Then
                fColumnSum = 0
            ElseIf ((Z >= 1) And (Z < (n - (R - 1)))) Then
                ColumnSum = 0
                For a = 1 To Z
                    ColumnSum = ColumnSum + Cdist(n, R, 1, a)
                Next a
                fColumnSum = ColumnSum
            ElseIf (Z >= (n - (R - 1))) Then
                fColumnSum = Comb(n, R)
            End If
            Exit Function
        exitfunction:
            fColumnSum = -1
        End Function

        Function Index2Combin(ByVal n As Integer, ByVal R As Integer, ByVal i As Double) As String
            On Error GoTo exitfunction
            Dim a, b, Combination(), Z As Integer
            Dim C, j As Double
            ReDim Combination(R)
            Dim tmpString, CombinFormat As String
            Dim NumberFound As Boolean
            tmpString = ""
            CombinFormat = ""
            C = Comb(n, R)
            j = i
            j = j - 1
            Z = 0
            b = Len(Format(n, "0"))
            For a = 1 To b
                CombinFormat = CombinFormat & "0"
            Next a
            For a = 1 To R
                If ((i >= 1) And (i <= C)) Then
                    If (a = 1) Then
                        Combination(a) = 1
                    Else
                        Combination(a) = Combination(a - 1) + 1
                    End If
                    NumberFound = False
                    Do
                        Select Case (j - fColumnSum((n - Z), (R - (a - 1)), (Combination(a) - (Z + 1))))
                            Case Is < 0
                                Combination(a) = Combination(a) - 1
                                NumberFound = True
                            Case Is = 0
                                NumberFound = True
                            Case Is > 0
                                Combination(a) = Combination(a) + 1
                        End Select
                    Loop Until NumberFound
                    j = j - fColumnSum((n - Z), (R - (a - 1)), (Combination(a) - (Z + 1)))
                    Z = Combination(a)
                Else
                    Combination(a) = 0
                End If
                tmpString = tmpString & Format(Combination(a), CombinFormat)
                If (a < R) Then tmpString = tmpString & " "
            Next a
            Index2Combin = tmpString
            Exit Function
        exitfunction:
            Index2Combin = "err"
        End Function

        Function Combin2Index(ByVal n As Integer, ByVal R As Integer, ByVal theRange As Range) As Double
            On Error GoTo exitfunction
            Dim a As Integer
            Dim fSum As Double
            Dim NotInAscendingOrder, NotInPool As Boolean
            NotInAscendingOrder = False
            NotInPool = False
            If ((theRange.Rows.Count <> 1) Or (theRange.Columns.Count <> R)) Then
                Combin2Index = -1
                Exit Function
            End If
            For a = 1 To R
                If (a < R) Then
                    If (theRange.Cells(1, a) >= theRange.Cells(1, (a + 1))) Then
                        NotInAscendingOrder = True
                    End If
                End If
                If ((theRange.Cells(1, a) < 1) Or (theRange.Cells(1, a) > n)) Then
                    NotInPool = True
                End If
            Next a
            If (NotInAscendingOrder Or NotInPool) Then
                Combin2Index = -1
                Exit Function
            End If
            fSum = 1
            For a = 1 To R
                If (a = 1) Then
                    fSum = fSum + fColumnSum(n, R, (theRange.Cells(1, 1) - 1))
                Else
                    fSum = fSum + fColumnSum((n - theRange.Cells(1, (a - 1))), (R - (a - 1)), (theRange.Cells(1, a) - (theRange.Cells(1, (a - 1)) + 1)))
                End If
            Next a
            Combin2Index = fSum
            Exit Function
        exitfunction:
            Combin2Index = -1
        End Function
        ____________________________________________________________________________________________________

        LOL, that looks more complicated than Chinese to me.

        Im still counting with my fingers.

          JADELottery's avatar - MeAtWork 03.PNG
          The Quantum Master
          West Concord, MN
          United States
          Member #21
          December 7, 2001
          3675 Posts
          Offline
          Posted: December 31, 2015, 4:52 pm - IP Logged

          LOL, that looks more complicated than Chinese to me.

          Im still counting with my fingers.

          Yep.

          Hence, the files we made.

          The files can be found here:

          Excel 2007 - ftp://www.jadexcode.com/Excel/CombinatorialIndex.xlsm

          Excel 2003 - ftp://www.jadexcode.com/Excel/CombinatorialIndex.xls

          These have function description and usage in the Function Information tab.

          =Fact(N)
          Returns -
          - An integer
          - The factorial of N, mathematically written as ' N! '
          - N!
          - N · (N - 1) · (N - 2) · … · 3 · 2 · 1
          - 0! = 1
          =Perm(N, R)
          Returns -
          - An integer
          - Using the Fact(N) function
          - The number of permutations in a pool of N numbers taken R at a time
          - (N! / (N - R)!)
          =Comb(N, R)
          Returns -
          - An integer
          - Using the Perm(N, R) and Fact(N) functions
          - The number of combinations in a pool of N numbers taken R at a time
          - (Perm(N, R) / Fact(R))
          - (Perm(N, R) / R!)
          - ((N! / (N - R)!) / R!)
          - (N! / (R! · (N - R)!))
          =Cdist(N, R, C, Z)
          Returns -
          - An integer
          - Using the Comb(N, R) function
          - The occurrence count of a number Z in a column C within a pool of N numbers taken R at a time
          - Comb((Z - 1), (C - 1)) · Comb((N - Z), (R - C))
          - (((Z - 1)! / ((C - 1)! · (Z - 1 - (C - 1))!) · ((N - Z)! / ((R - C)! · (N - Z - (R - C))!)))
          - ((Z - 1)! · (N - Z)!) / ((C - 1)! · (Z - C)! · (R - C)! · (N - Z - R +C)!)
          =fColumnSum(N, R, Z)
          Returns -
          - An integer
          - Using the Cdist(N, R, C, Z) and Comb(N, R) functions
          - The sum of occurrence counts in the first column, 1, from the first number 1 to a number Z
          =Index2Combin(N, R, Index)
          Returns -
          - A string
          - Using the fColumnSum(N, R, Z) and Comb(N, R) functions
          - A Combination based on an Index in a pool of N numbers taken R at a time
          - 00's for an error condition
          =Combin2Index(N, R, Range)
          Returns -
          - An integer
          - Using the fColumnSum(N, R, Z) function
          - An Index value from a Combination within a pool of N numbers taken R at a time
          - A -1 for an error condition
          Variables and Array
          N - Pool Size, positive integer
          R - Pick Size, positive integer
          C - Column, positive integer
          Z - Number, positive integer
          Index - A positive integer index value within a combination of N numbers taken R at a time
          Range - An array of positive integer values in ascending order left to right; in a single row containing a combination of N numbers taken R at a time

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          Any gain or loss is your responsibility.
          Use at your own risk.

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            lakerben's avatar - spherewall
            New Mexico
            United States
            Member #86099
            January 29, 2010
            11115 Posts
            Offline
            Posted: December 31, 2015, 7:02 pm - IP Logged

            Yep.

            Hence, the files we made.

            The files can be found here:

            Excel 2007 - ftp://www.jadexcode.com/Excel/CombinatorialIndex.xlsm

            Excel 2003 - ftp://www.jadexcode.com/Excel/CombinatorialIndex.xls

            These have function description and usage in the Function Information tab.

            =Fact(N)
            Returns -
            - An integer
            - The factorial of N, mathematically written as ' N! '
            - N!
            - N · (N - 1) · (N - 2) · … · 3 · 2 · 1
            - 0! = 1
            =Perm(N, R)
            Returns -
            - An integer
            - Using the Fact(N) function
            - The number of permutations in a pool of N numbers taken R at a time
            - (N! / (N - R)!)
            =Comb(N, R)
            Returns -
            - An integer
            - Using the Perm(N, R) and Fact(N) functions
            - The number of combinations in a pool of N numbers taken R at a time
            - (Perm(N, R) / Fact(R))
            - (Perm(N, R) / R!)
            - ((N! / (N - R)!) / R!)
            - (N! / (R! · (N - R)!))
            =Cdist(N, R, C, Z)
            Returns -
            - An integer
            - Using the Comb(N, R) function
            - The occurrence count of a number Z in a column C within a pool of N numbers taken R at a time
            - Comb((Z - 1), (C - 1)) · Comb((N - Z), (R - C))
            - (((Z - 1)! / ((C - 1)! · (Z - 1 - (C - 1))!) · ((N - Z)! / ((R - C)! · (N - Z - (R - C))!)))
            - ((Z - 1)! · (N - Z)!) / ((C - 1)! · (Z - C)! · (R - C)! · (N - Z - R +C)!)
            =fColumnSum(N, R, Z)
            Returns -
            - An integer
            - Using the Cdist(N, R, C, Z) and Comb(N, R) functions
            - The sum of occurrence counts in the first column, 1, from the first number 1 to a number Z
            =Index2Combin(N, R, Index)
            Returns -
            - A string
            - Using the fColumnSum(N, R, Z) and Comb(N, R) functions
            - A Combination based on an Index in a pool of N numbers taken R at a time
            - 00's for an error condition
            =Combin2Index(N, R, Range)
            Returns -
            - An integer
            - Using the fColumnSum(N, R, Z) function
            - An Index value from a Combination within a pool of N numbers taken R at a time
            - A -1 for an error condition
            Variables and Array
            N - Pool Size, positive integer
            R - Pick Size, positive integer
            C - Column, positive integer
            Z - Number, positive integer
            Index - A positive integer index value within a combination of N numbers taken R at a time
            Range - An array of positive integer values in ascending order left to right; in a single row containing a combination of N numbers taken R at a time

            Impressive!

            Happy new year Jade!

            How about them cowboys!

             

             

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              SergeM's avatar - slow icon.png
              Economy class
              Belgium
              Member #123700
              February 27, 2012
              4035 Posts
              Offline
              Posted: January 1, 2016, 2:28 pm - IP Logged
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                bgonçalves
                Brasil
                Member #92564
                June 9, 2010
                2122 Posts
                Offline
                Posted: January 2, 2016, 5:52 am - IP Logged

                Jaden, you can create a macro on the following criteria
                Most = 02 = 01 Less Equal = 00 Always the last draw for the next Example
                15 23 35 45 02 52                  02 code
                05 18 29 38 48 59
                already is 01 (less)
                01 13 20 32 42 51 or other smaller or the larger numbers also