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## 5/n lotteries Edit

• In Pennsylvania, there is a 5/30 lottery called Treasure Hunt, where you must pick 5 numbers out of 30. Therefore, the number of possible combinations is equal to 30C5 = 142,506.
• Its prime factorization is 2 × 33 × 7 × 13 × 29.
• In Virginia, there is a 5/34 lottery called Cash 5, where you must pick 5 numbers out of 34. Therefore, the number of possible combinations is equal to 34C5 = 278,256.
• Its prime factorization is 24 × 3 × 11 × 17 × 31.
• In Russia, there is a 5/36 lottery, where you must pick 5 numbers out of 36. Therefore, the number of possible combinations is equal to 36C5 = 376,992.
• Its prime factorization is 25 × 32 × 7 × 11 × 17.
• In New York, there is a 5/39 lottery called Take 5, where you must pick 5 numbers out of 39. Therefore, the number of possible combinations is equal to 39C5 = 575,757.
• Its prime factorization is 32 × 7 × 13 × 19 × 37.
• In Iceland, there is a 5/40 lottery, where you must pick 5 numbers out of 40. Therefore, the number of possible combinations is equal to 40C5 = 658,008.
• Its prime factorization is 23 × 32 × 13 × 19 × 37.
• In North Carolina, there is a 5/41 lottery called Carolina Cash 5, where you must pick 5 numbers out of 41. Therefore, the number of possible combinations is equal to 41C5 = 749,398.
• Its prime factorization is 2 × 13 × 19 × 37 × 41.
• In the U.S. state of Georgia, there is a 5/42 lottery called Fantasy 5, where you must pick 5 numbers out of 42. Therefore, the number of possible combinations is equal to 42C5 = 850,668.
• Its prime factorization is 22 × 3 × 7 × 13 × 19 × 41.
• In Pennsylvania, there is a 5/43 lottery called Cash 5, where you must pick 5 numbers out of 43. Therefore, the number of possible combinations is equal to 43C5 = 962,598.
• Its prime factorization is 2 × 3 × 7 × 13 × 41 × 43.
• In Ukraine, there is a 5/45 lottery, where you must pick 5 numbers out of 45. Therefore, the number of possible combinations is equal to 45C5 = 1,221,759.
• Its prime factorization is 32 × 7 × 11 × 41 × 43.
• In Uruguay, there is a 5/48 lottery, where you must pick 5 numbers out of 48. Therefore, the number of possible combinations is equal to 48C5 = 1,712,304.
• Its prime factorization is 24 × 32 × 11 × 23 × 47.
• In the card game of poker, a poker hand can be any combination of 5 cards of a standard 52-card deck. Therefore, the number of possible combinations is equal to 52C5 = 2,598,960.
• It is also equal to the number of possible combinations in a 5/52 lottery available in some U.S. states, such as Arizona, Indiana and Kentucky, where you must pick 5 cards out of 52, or they are generated by a terminal.
• Its prime factorization is 24 × 3 × 5 × 72 × 13 × 17.
• In some countries, such as Italy, there is a 5/90 lottery, where you must pick 5 numbers out of 90. The number of possible combinations is equal to 90C5 = 43,949,268.
• Its prime factorization is 22 × 32 × 11 × 29 × 43 × 89.

## 6/n lotteries Edit

• In the country of Georgia, there is a 6/36 lottery, where you must pick 6 numbers out of 36. Therefore, the number of possible combinations is equal to 36C6 = 1,947,792.
• Its prime factorization is 24 × 3 × 7 × 11 × 17 × 31.
• In New Zealand, there is a 6/40 lottery called Lotto, where you must pick 6 numbers out of 40. Therefore, the number of possible combinations is equal to 40C6 = 3,838,380.
• Its prime factorization is 22 × 3 × 5 × 7 × 13 × 19 × 37.
• In the Philippines, there is a 6/42 lottery, where you must pick 6 numbers out of 42. Therefore, the number of possible combinations is equal to 42C6 = 5,245,786.
• Its prime factorization is 2 × 7 × 13 × 19 × 37 × 41.
• In Japan, there is a 6/43 lottery, where you must pick 6 numbers out of 43. Therefore, the number of possible combinations is equal to 43C6 = 6,096,454.
• Its prime factorization is 2 × 7 × 13 × 19 × 41 × 43.
• In some countries, such as the Netherlands, there is a 6/45 lottery, where you must pick 6 numbers out of 45. The number of possible combinations is equal to 45C6 = 8,145,060.
• Its prime factorization is 22 × 3 × 5 × 7 × 11 × 41 × 43.
• In the Republic of Ireland, there is a 6/47 lottery, where you must pick 6 numbers out of 47. Therefore, the number of possible combinations is equal to 47C6 = 10,737,573.
• Its prime factorization is 3 × 7 × 11 × 23 × 43 × 47.
• In some countries, such as Germany, there is a 6/49 lottery, where you must pick 6 numbers out of 49. The number of possible combinations is equal to 49C6 = 13,983,816.
• Its prime factorization is 23 × 3 × 72 × 11 × 23 × 47.
• In some countries, such as South Africa and Ukraine, there is a 6/52 lottery, where you must pick 6 numbers out of 52. Therefore, the number of possible combinations is equal to 52C6 = 20,358,520.
• Its prime factorization is 23 × 5 × 72 × 13 × 17 × 47.
• In Florida, there is a 6/53 lottery called Florida Lotto, where you must pick 6 numbers out of 53. Therefore, the number of possible combinations is equal to 53C6 = 22,957,480.
• Its prime factorization is 23 × 5 × 72 × 13 × 17 × 53.
• In Texas, there is a 6/54 lottery called Lotto Texas, where you must pick 6 numbers out of 54. Therefore, the number of possible combinations is equal to 54C6 = 25,827,165.
• Its prime factorization is 32 × 5 × 72 × 13 × 17 × 53.
• In the Philippines, there is a 6/55 lottery, where you must pick 6 numbers out of 55. Therefore, the number of possible combinations is equal to 55C6 = 28,989,675.
• Its prime factorization is 32 × 52 × 11 × 13 × 17 × 53.
• In Mexico, there is a 6/56 lottery, where you must pick 6 numbers out of 56. Therefore, the number of possible combinations is equal to 56C6 = 32,468,436.
• Its prime factorization is 22 × 32 × 7 × 11 × 13 × 17 × 53.
• In the Philippines, there is a 6/58 lottery, where you must pick 6 numbers out of 58. Therefore, the number of possible combinations is equal to 58C6 = 40,475,358.
• Its prime factorization is 2 × 32 × 7 × 11 × 19 × 29 × 53.
• In the United Kingdom, there is a 6/59 lottery, where you must pick 6 numbers out of 59. The number of possible combinations is equal to 59C6 = 45,057,474.
• Its prime factorization is 2 × 32 × 7 × 11 × 19 × 29 × 59.
• In Brazil, there is a 6/60 lottery called Mega-Sena, where you must pick 6 numbers out of 60. Therefore, the number of possible combinations is equal to 60C6 = 50,063,860.
• Its prime factorization is 22 × 5 × 7 × 11 × 19 × 29 × 59.
• In Italy, there is a 6/90 lottery, where you must pick 6 numbers out of 90. The number of possible combinations is equal to 90C6 = 622,614,630.
• Its prime factorization is 2 × 3 × 5 × 11 × 17 × 29 × 43 × 89.

## 7/n lotteries Edit

• In Norway, there is a 7/34 lottery, where you must pick 7 numbers out of 34. The number of possible combinations is equal to 34C7 = 5,379,616.
• Its prime factorization is 25 × 11 × 17 × 29 × 31.
• In Sweden, there is a 7/35 lottery, where you must pick 7 numbers out of 35. The number of possible combinations is equal to 35C7 = 6,724,520.
• Its prime factorization is 23 × 5 × 11 × 17 × 29 × 31.
• In Denmark, there is a 7/36 lottery, where you must pick 7 numbers out of 36. The number of possible combinations is equal to 36C7 = 8,347,680.
• Its prime factorization is 25 × 32 × 5 × 11 × 17 × 31.
• In some countries, such as Finland, Serbia and Slovenia, there is a 7/39 lottery, where you must pick 7 numbers out of 39. The number of possible combinations is equal to 39C7 = 15,380,937.
• Its prime factorization is 32 × 11 × 13 × 17 × 19 × 37.
• In Australia, there is a 7/45 lottery called Oz Lotto, where you must pick 7 numbers out of 45. Therefore, the number of possible combinations is equal to 45C7 = 45,379,620.
• Its prime factorization is 22 × 32 × 5 × 11 × 13 × 41 × 43.
• In Canada, there is a 7/49 lottery called Lotto Max, where you must pick 7 numbers out of 49. Therefore, the number of possible combinations is equal to 49C7 = 85,900,584.
• Its prime factorization is 23 × 3 × 7 × 11 × 23 × 43 × 47.

## Other single-drum lotteries Edit

• In the U.S. state of Washington, there is a 4/24 lottery called Match 4, where you must pick 4 numbers out of 24. Therefore, the number of possible combinations is equal to 24C4 = 10,626.
• Its prime factorization is 2 × 3 × 7 × 11 × 23.
• In New Zealand, there is a 4/40 lottery called Lotto Strike, where you must pick 4 numbers out of 40 in the correct order. Therefore, the number of possible combinations is equal to 40P4 = 2,193,360.
• Its prime factorization is 24 × 3 × 5 × 13 × 19 × 37.
• In parts of the United States, there is a 12/24 lottery called All or Nothing, where you must pick 12 numbers out of 24. Therefore, the number of possible combinations is equal to 24C12 = 2,704,156.
• Its prime factorization is 22 × 7 × 13 × 17 × 19 × 23.
• In Venezuela, there is a 15/25 lottery, where you must pick 15 numbers out of 25. Therefore, the number of possible combinations is equal to 25C15 = 3,268,760.
• Its prime factorization is 23 × 5 × 11 × 17 × 19 × 23.
• In the Czech republic, there is a lottery named Šťastných 10 (literally "Happy 10"), where you pick 1-10 numbers of 80. When it draws, 20 numbers of 80 numbers are drawn. The number of possible combination of the drawing is 80C20 = 3,535,316,142,212,174,320 (3 and a half quintillion combinations in short scale, or 3 and a half trillion combinations in long scale).[1]
• The table of chances is given below: (The table is written in Czech Koruna, where 1£ ~ 28 Kč and 1\$ ~ 22 Kč)
 Number of judged combinations ✖ 10 9 8 7 6 5 4 3 2 1 10 200,000× 9 10,000× 50,000× 8 500× 2,000× 20,000× 7 20× 200× 400× 4,000× 6 10× 20× 40× 100× 600× 5 3× 3× 4× 10× 20× 200× 4 Nothing Nothing 1× 2× 2× 16× 50× 3 Nothing Nothing Nothing Nothing 1× 2× 8× 16× 2 Nothing Nothing Nothing Nothing Nothing Nothing Nothing 2× 8× 1 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing 2× 0 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing
• Its prime factorization is 24 × 5 × 7 × 11 × 13 × 23 × 31 × 37 × 61 × 67 × 71 × 73 × 79.
• In parts of Australia, there is a 4/45 lottery called Lotto Strike, where you must pick 4 numbers out of 45 in the correct order. Therefore, the number of possible combinations is equal to 45P4 = 3,575,880.
• Its prime factorization is 23 × 33 × 5 × 7 × 11 × 43.
• In Australia, there is a 8/37 lottery called Set For Life, where you must pick 8 numbers out of 37. Therefore, the number of possible combinations is equal to 37C8 = 38,608,020.
• Its prime factorization is 22 × 32 × 5 × 11 × 17 × 31 × 37.
• In Chile, there is a 14/25 lottery, where you must pick 14 numbers out of 25. Therefore, the number of possible combinations is equal to 25C14 = 4,457,400.
• Its prime factorization is 23 × 3 × 52 × 17 × 19 × 23.

## Mega Ball lotteries Edit

• In Canada, there is a 5/49+1/7 lottery called Daily Grand, where you must pick 5 numbers out of 49, and 1 number out of 7. Therefore, the number of possible combinations is equal to 5C49 × 7 = 13,348,188.
• Its prime factorization is 22 × 32 × 73 × 23 × 47.
• In Germany, there is a 6/49+1/10 lottery, where you must pick 6 numbers out of 49, and the final digit of the serial number is used for determining the top prize. Therefore, the number of possible combinations is 49C6 × 10. In some other Western European countries, there is a 5/50+2/12 lottery called EuroMillions, where you must pick 5 numbers out of 50, and 2 numbers out of 12. Therefore, the number of possible combinations is 50C5 × 12C2. Both 49C6 × 10 and 50C5 × 12C2 are equal to 139,838,160.
• Its prime factorization is 24 × 3 × 5 × 72 × 11 × 23 × 47.
• In Colombia, there is a 5/43+1/16 lottery, where you must pick 5 numbers out of 43, and 1 number out of 16. Therefore, the number of possible combinations is equal to 43C5 × 16 = 15,401,568.
• Its prime factorization is 25 × 3 × 7 × 13 × 41 × 43.
• In Israel, there is a 6/37 + 1/7 lottery, where you must pick 6 numbers out of 37, and 1 number out of 7. The number of possible combinations is equal to 37C6 × 7 = 16,273,488.
• Its prime factorization is 24 × 3 × 72 × 11 × 17 × 37.
• In France, there is a 5/49+1/10 lottery, where you must pick 5 numbers out of 49, and 1 number out of 10. Therefore, the number of possible combinations is equal to 5C49 × 10 = 19,068,840.
• Its prime factorization is 23 × 32 × 5 × 72 × 23 × 47.
• In parts of the United States, there is a 5/60+1/4 lottery called Cash4Life, where you must pick 5 numbers out of 60, and 1 number out of 4. Therefore, the number of possible combinations is equal to 60C5 × 4 = 21,846,048.
• Its prime factorization is 25 × 3 × 7 × 19 × 29 × 59.
• In Argentina, there is a 6/42+2/10 lottery, where you must pick 6 numbers out of 42, and 2 numbers out of 10. Therefore, the number of possible combinations is equal to 42C6 × 10C2 = 236,060,370.
• Its prime factorization is 2 × 32 × 5 × 7 × 13 × 19 × 37 × 41.
• In South Africa, there is a 5/45 + 1/20 lottery, where you must pick 5 numbers out of 45, and 1 number out of 20. Therefore, the number of possible combinations is equal to 45C5 × 20 = 24,435,180.
• Its prime factorization is 22 × 32 × 5 × 7 × 11 × 41 × 43.
• In Portugal, there is a 5/49+1/13 lottery, where you must pick 5 numbers out of 49, and 1 number out of 13. Therefore, the number of possible combinations is equal to 5C49 × 13 = 24,789,492.
• Its prime factorization is 22 × 32 × 72 × 13 × 23 × 47.
• In the United States, there is a 5/75+1/15 lottery called Mega Millions, where you must pick 5 numbers out of 75, and 1 number out of 15. Therefore, the number of possible combinations is equal to 75C5 × 15 = 258,890,850.
• Its prime factorization is 2 × 33 × 52 × 37 × 71 × 73.
• In parts of the United States, there is a 5/47+1/19 lottery called Hot Lotto, where you must pick 5 numbers out of 47, and 1 number out of 19. Therefore, the number of possible combinations is equal to 47C5 × 19 = 29,144,841.
• Its prime factorization is 3 × 11 × 19 × 23 × 43 × 47.
• In the United States, there is a 5/69+1/26 lottery called Powerball, where you must pick 5 numbers out of 69, and 1 number out of 26. Therefore, the number of possible combinations is equal to 69C5 × 26 = 292,201,338.
• Its prime factorization is 2 × 3 × 11 × 132 × 17 × 23 × 67.
• In Croatia, there is a 7/39 + 1/2 lottery, where you must pick 7 numbers out of 39, and 1 letter out of 2. The number of possible combinations is equal to 39C7 × 2 = 30,761,874.
• Its prime factorization is 2 × 32 × 11 × 13 × 17 × 19 × 37.
• In parts of the United States, there is a 5/48+1/18 lottery called Lucky for Life, where you must pick 5 numbers out of 48, and 1 number out of 18. Therefore, the number of possible combinations is equal to 48C5 × 18 = 30,821,472.
• Its prime factorization is 25 × 34 × 11 × 23 × 47.
• In Switzerland, there is a 6/42 + 1/6 lottery, where you must pick 6 numbers out of 42, and 1 number out of 6. The number of possible combinations is equal to 42C6 × 6 = 31,474,716.
• Its prime factorization is 22 × 3 × 7 × 13 × 19 × 37 × 41.
• In Spain, there is a 5/54+1/10 lottery called El Gordo de la Primitiva, where you must pick 5 numbers out of 54, and 1 number out of 10. Therefore, the number of possible combinations is equal to 54C5 × 10 = 31,625,100.
• Its prime factorization is 22 × 33 × 52 × 13 × 17 × 53.
• In New Zealand, there is a 6/40+1/10 lottery called Powerball, where you must pick 6 numbers out of 40, and 1 number out of 10. Therefore, the number of possible combinations is equal to 40C6 × 10 = 38,383,800.
• Its prime factorization is 23 × 3 × 52 × 7 × 13 × 19 × 37.
• In California, there is a 5/47+1/27 lottery called SuperLotto Plus, where you must pick 5 numbers out of 47, and 1 number out of 27. Therefore, the number of possible combinations is equal to 47C5 × 27 = 41,416,353.
• Its prime factorization is 34 × 11 × 23 × 43 × 47.
• In the Netherlands, there is a 6/45 + 1/6 lottery, where you must pick 6 numbers out of 45, and 1 color out of 6. The number of possible combinations is equal to 45C6 × 6 = 48,870,360.
• Its prime factorization is 23 × 32 × 5 × 7 × 11 × 41 × 43.
• In Chile, there is a 7/30+1/3 lottery, where you must pick 7 numbers out of 30, and 1 number out of 3. Therefore, the number of possible combinations is equal to 30C7 × 3 = 6,107,400.
• Its prime factorization is 23 × 34 × 52 × 13 × 29.
• In Australia, there is a 6/40+1/20 lottery called Powerball, where you must pick 6 numbers out of 40, and 1 number out of 20. Therefore, the number of possible combinations is equal to 40C6 × 20 = 76,767,600.
• Its prime factorization is 24 × 3 × 52 × 7 × 13 × 19 × 37.
• In the United Kingdom, there is a 5/39+1/14 lottery called Thunderball, where you must pick 5 numbers out of 39, and 1 number out of 14. Therefore, the number of possible combinations is equal to 39C14 × 10 = 8,060,598.
• Its prime factorization is 2 × 32 × 72 × 13 × 19 × 37.
• In Germany and some other European countries, there is a 5/50+2/10 lottery called Eurojackpot, where you must pick 5 numbers out of 50, and 2 numbers out of 10. Therefore, the number of possible combinations is equal to 50C5 × 10C2 = 95,344,200.
• Its prime factorization is 23 × 32 × 52 × 72 × 23 × 47.
• In Northern Europe, there is a 6/48+1/8 lottery called Viking Lotto, where you must pick 6 numbers out of 48, and 1 number out of 8. Therefore, the number of possible combinations is equal to 48C6 × 8 = 98,172,096.
• Its prime factorization is 26 × 3 × 11 × 23 × 43 × 47.

## Other multi-drum lotteries Edit

• In Slovenia, there is a (3/8)*3 lottery, where you must pick three fields with 3 numbers out of 8. Therefore, the number of possible combinations is equal to (8C3)3 = 175,616.
• Its prime factorization is 29 × 73.
• In Russia, there is a (4/20)*2 lottery, where you must pick two fields with 4 numbers out of 20. Therefore, the number of possible combinations is equal to (20C4)2 = 23,474,025.
• Its prime factorization is 32 × 52 × 172 × 192.

## Expressions in other bases Edit

• 8,060,598:
• In binary, 111 1010 1111 1110 1011 0110

## Approximations Edit

Approximations for 8,060,598
Notation Approximation
Scientific notation $$8.0606*10^{6}$$
Arrow notation $$2,839↑ 2<n<2,840↑ 2$$
Chained arrow notation $$2,839→ 2<n<2,840→ 2$$
BEAF $$\{2839,2\}$$
Hyperfactorial array notation $$10!$$
Fast-growing hierarchy $$f_2(19)$$
Hardy hierarchy $$H_{\omega^2}(19)$$
Slow-growing hierarchy $$g_{\omega^2}(2,839)$$

## Sources Edit

1. Šťastných 10 – pravidla, šance na výhru (in Czech)