Lottery Pairs Formula

[ststern45]

Hello everyone,

I wanted to ask if how to calculate how many times a number appears with a second number in a lottery game.
For example, in a 5/30 game how many times does the number 2 appear with the number 1 in the second position?
I know I could create a worksheet with all 142506 possible sets then filter numbers by positions which would result in 3276 total times the number 1 in position 1 and a number 2 in position 2.
How many times the number 1 in position 1 and number 3 in position 3 which is 351?

Thank you.

 

[bebo021999]

Could you give a few combination cases of 1 in post 1 and 2 in post 2? and 1 in pos 1 and 3 in post 3?
Is it correct (with dupplicate)
1 2 5 8 10
1 2 20 20 30
and
1 5 3 15 18
1 6 3 30 30

???

 

[ststern45]

Can the following code be changed to calculate Pairs?

StephenCrump post from 2013

How to calculate lottery combinations by sums

Hello, Is there any way to calculate sum combinations? Simple for example 6/49 lottery total combinations 13.983.816 Using all 49 numbers…. Minimum sum 1+2+3+4+5+6 = 21 (1 combination) Maximum sum 44+45+46+47+48+49= 279 (1 combination) Question-1 how much combinations will be find with each...

www.mrexcel.com

Sub Test2()

Dim N As Long, r As Long, lResults() As Long, lTally() As Long, lSmall As Long, lLarge As Long
Dim lTemp As Long, i As Long, j As Long, lFirst As Long
Dim rngPaste As Range

N = 30
r = 5
lSmall = r * (r + 1) / 2
lLarge = r * (2 * N - r + 1) / 2
ReDim lTally(lSmall To lLarge, 1 To N - r + 2)
For i = lSmall To lLarge
lTally(i, 1) = i
Next i

Set rngPaste = Range("A1")
On Error Resume Next
Range("Tallies").Clear
On Error GoTo 0
With rngPaste
.Value = "Sum"
.Offset(, 1).Value = "Frequencies"
With .Offset(1, 1).Resize(, UBound(lTally, 2) - 1)
.Formula = "=Column()-Column(" & rngPaste.Address(, True) & ")"
.NumberFormat = "0"" first"""
End With
.Resize(2).EntireRow.Font.Bold = True
End With

For lFirst = 1 To N - r + 1

lResults = GetCombinations(N - lFirst, r - 1)

For i = 1 To UBound(lResults)
lTemp = 0
For j = 1 To r - 1
lTemp = lTemp + lResults(i, j)
Next j
lTally(lTemp + r * lFirst, 1 + lFirst) = lTally(lTemp + r * lFirst, 1 + lFirst) + 1
Next i

Next lFirst

With rngPaste
.Resize(lLarge - lSmall + 3, UBound(lTally, 2)).Name = "Tallies"
.Offset(2).Resize(lLarge - lSmall + 1, UBound(lTally, 2)).Value = lTally
End With

End Sub

Function GetCombinations(lNumber As Long, lNoChosen As Long) As Long()

Dim lOutput() As Long, lCombinations As Long
Dim i As Long, j As Long, k As Long

lCombinations = WorksheetFunction.Combin(lNumber, lNoChosen)
ReDim lOutput(1 To lCombinations, 1 To lNoChosen)

For i = 1 To lNoChosen
lOutput(1, i) = i
Next i

For i = 2 To lCombinations
For j = 1 To lNoChosen
lOutput(i, j) = lOutput(i - 1, j)
Next j
For j = lNoChosen To 1 Step -1
lOutput(i, j) = lOutput(i, j) + 1
If lOutput(i, j) <= lNumber - (lNoChosen - j) Then Exit For
Next j
For k = j + 1 To lNoChosen
lOutput(i, k) = lOutput(i, k - 1) + 1
Next k
Next i

GetCombinations = lOutput

End Function

 

[motilulla]

Hello everyone,

I wanted to ask if how to calculate how many times a number appears with a second number in a lottery game.
For example, in a 5/30 game how many times does the number 2 appear with the number 1 in the second position?
I know I could create a worksheet with all 142506 possible sets then filter numbers by positions which would result in 3276 total times the number 1 in position 1 and a number 2 in position 2.
How many times the number 1 in position 1 and number 3 in position 3 which is 351?

Thank you.

Hello ststern45, may the link below help

Formula calculate combination of each number by there 5 positions

Hello, I want to know how much combinations could be each of number by there 5 positions. I find the formula which can gives the combination of each number only in the first position formula E6=COMBIN(50-D6,4) Copied down to E51. My query is how much combination could be for each number within...

www.mrexcel.com

Regards,
Moti

 

[motilulla]

here is the layout...

Libro1
	A	B	C	D	E	F
1
2
3		Position
4	Number	1	2	3	4	5
5	1	23751	0	0	0	0
6	2	20475	3276	0	0	0
7	3	17550	5850	351	0	0
8	4	14950	7800	975	26	0
9	5	12650	9200	1800	100	1
10	6	10626	10120	2760	240	5
11	7	8855	10626	3795	460	15
12	8	7315	10780	4851	770	35
13	9	5985	10640	5880	1176	70
14	10	4845	10260	6840	1680	126
15	11	3876	9690	7695	2280	210
16	12	3060	8976	8415	2970	330
17	13	2380	8160	8976	3740	495
18	14	1820	7280	9360	4576	715
19	15	1365	6370	9555	5460	1001
20	16	1001	5460	9555	6370	1365
21	17	715	4576	9360	7280	1820
22	18	495	3740	8976	8160	2380
23	19	330	2970	8415	8976	3060
24	20	210	2280	7695	9690	3876
25	21	126	1680	6840	10260	4845
26	22	70	1176	5880	10640	5985
27	23	35	770	4851	10780	7315
28	24	15	460	3795	10626	8855
29	25	5	240	2760	10120	10626
30	26	1	100	1800	9200	12650
31	27		26	975	7800	14950
32	28			351	5850	17550
33	29				3276	20475
34	30					23751
Sheet2

Cell Formulas
Range	Formula
F5:F34,E5:E33,D5:D32,C5:C31,B5:B30	B5	=IF(B$4>$A5,0,COMBIN($A5-1,B$4-1)*COMBIN(30-$A5,5-B$4))

 

[ststern45]

Thank you to both of you.