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Combinations, Sets for Frequency System: Lotto 5/39, Lotto 6/49, Pick-3, Pick-4

By Ion Saliu, Founder of: Lottery Mathematics, Lotto Programming Science

Win any lottery game with lotto strategies, systems for numbers frequency.

Calculate total combinations from groups of numbers in jackpot lotto games.

Jackpot Lotto: Calculate Combinations from 3 Groups of Numbers
Pick 3 4 Lotteries: Calculate Sets from 3 Groups of Numbers
Pick 5 Lottery: Calculate ALL Sets in Quinto Lottery
Resources in Lottery Software, Strategies, Lotto Systems

Special lottery software: SkipDecaFreq, programs in the Bright / Ultimate application bundles.

Calculate sets of digits in pick lotteries: singles, doubles, triples, quads.

Jackpot Lotto: Calculate Combinations from 3 Groups of Numbers

We divided the lotto numbers (jackpot games) in 3 groups of N1, N2, and N3 numbers. We work here with 2 lotto games that draw K numbers: K = 5 and K = 6. The lotto numbers are unique in each group: There is no overlap. We apply the combination formula to each group and finally multiply the 3 results.

C(N, M) is the general formula for combinations of N numbers taken M at a time.

                    N*(N-1)*(N-2)*(N-3)* ... *(N-M+1)
C(N, M) = -----------------------------------------------
                  1*2*3* ... *M

The following tables show the amount of lottery combinations from 3 groups of numbers ordered by frequency. Lotto games analyzed: 5/39 and 6/49.

Lotto 5/39 Combinations for Frequency System

Group_1 = 5 #s

Group_2 = 14 #s

Group_3 = 20 #s

Total Combos

0 0 5 15504
0 5 0 2002
5 0 0 1
0 1 4 67830
0 4 1 20020
1 0 4 24225
1 4 0 5005
4 0 1 100
4 1 0 70
0 2 3 103740
0 3 2 69160
2 0 3 11400
2 3 0 3640
3 0 2 1900
3 2 0 910
1 1 3 79800
1 3 1 36400
3 1 1 2800
1 2 2 86450
2 1 2 26600
2 2 1 18200
Total C(39, 5) ~ ~ 575757

All lotto 649 combinations total 13983816 divided in 3 groups of numbers.

Lotto 6/49 Combinations for Frequency System

Group_1 = 6 #s

Group_2 = 18 #s

Group_3 = 25 #s

Total Combos

0 0 6 177100
0 6 0 18564
6 0 0 1
0 1 5 956340
0 5 1 214200
1 0 5 318780
1 5 0 51408
5 0 1 150
5 1 0 108
0 2 4 1935450
0 4 2 918000
2 0 4 189750
2 4 0 45900
4 0 2 4500
4 2 0 2295
1 1 4 1366200
1 4 1 459000
4 1 1 6750
0 3 3 1876800
3 0 3 46000
3 3 0 16320
1 2 3 2111400
1 3 2 1468800
2 1 3 621000
2 3 1 306000
3 1 2 108000
3 2 1 76500
2 2 2 688500
Total C(49, 6) ~ ~ 13983816

Pick-3 Strategy, System, Systems, Frequency, all 1000 sets.

Pick Lotteries: Calculate Sets from 3 Groups of Digits

Although the odds are much lower, calculations in pick (digit, daily games) lotteries are more complex. The sets in these games have not only unique digits (as in jackpot lotto), but also repeat digits (doubles, triples, quadruples).

I. Calculating total unique sets is the easiest part. Total digits: N = 10; digits per set M = 3 (pick-3) or M = 4 (pick-4):

II. Calculating total duplicate sets is more complicated and involves more steps. The calculations are different from one type of duplication to another (doubles, triples, quadruples, quads).

Pick-3 Sets for Frequency System

Group_1
2 digits

Group_2
3 digits

Group_3
5 digits

Single
Sets

Double
Sets

Triple
Sets

Total
Sets

0 0 3 60 60 5 125
0 3 0 6 18 3 27
3 0 0 0 6 2 8
0 1 2 180 45 0 225
0 2 1 90 45 0 135
1 0 2 120 30 0 150
1 2 0 36 18 0 54
2 0 1 30 30 0 60
2 1 0 18 18 0 36
1 1 1 180 0 0 180
Total Pick-3 ~ ~ 720 270 10 1000

The pick-4 lottery sets, unique, straight, duplicates sum up to 10000.

Pick-4 Sets for Frequency System

Group_1
2 digits

Group_2
3 digits

Group_3
5 digits

Single
Sets

1-Pair
Sets

2-Pair
Sets

Triple+1
Sets

Quad
Sets

Total
Sets

0 0 4 120 360 60 80 5 625
0 4 0 0 36 18 24 3 81
4 0 0 0 0 6 8 2 16
0 1 3 720 720 0 60 0 1500
0 3 1 120 360 0 60 0 540
1 0 3 480 480 0 40 0 1000
1 3 0 48 144 0 24 0 216
3 0 1 0 120 0 40 0 160
3 1 0 0 72 0 24 0 96
1 1 2 1440 360 0 0 0 1800
1 2 1 720 360 0 0 0 1080
2 1 1 360 360 0 0 0 720
0 2 2 720 540 90 0 0 1350
2 0 2 240 300 60 0 0 600
2 2 0 72 108 36 0 0 216
Total Pick-4 ~ ~ 5040 4320 270 360 10 10000

Pick-5 Quinto sets total 100000, from straight or distinct 5 digits to quintets.

Pick 5 Lottery: Calculate ALL Sets in Quinto Lottery

Axiomatic one, I do not have a lot of software for pick 5 digit (Quinto) lottery. Therefore I will not divide the pick-5 digits in groups based on frequency. I will calculate only the total sets: Singles, 1 double + 3 singles, 2 doubles + 1 single, 1 triple + 2 singles, 1 triple + 1 double, 1 quadruple + 1 single, quintets.

There are fewer boxed sets than straight pick sets; download 3 free files here.

All Pick-5 Lottery Sets: Distinct and Duplicate

Singles

1 Double +
3 Singles

2 Doubles +
1 Single

1 Triple +
2 Singles

1 Triple +
1 Double

1 Quad +
1 Single

Quintets

TOTAL

30240

50400

10800

7200

900

450

10

100000

Table with all straight and duplicate sets in pick-5 quinto lottery games.

Boxed Pick-5 Lottery Sets

Singles

1 Double +
3 Singles

2 Doubles +
1 Single

1 Triple +
2 Singles

1 Triple +
1 Double

1 Quad +
1 Single

Quintets

TOTAL

252

840

360

360

90

90

10

2002

Lotto combinations, tables to work with frequency Lottery systems.

Resources in Lottery Software, Strategies, Lotto Systems

The correlation between frequency lotto groups and the number of lotto combinations.


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