Statistics

Problem Statement for "LotteryPyaterochka"

Problem Statement

Alice likes lotteries. Her favorite lottery is Pyaterochka, which is very popular in Belarus. Each ticket in this lottery is a rectangular grid with N rows and 5 columns, where each cell contains an integer between 1 and 5*N, inclusive. All integers within a single ticket are distinct.

After the tickets are distributed, the lottery organizers randomly choose 5 distinct integers, each between 1 and 5*N, inclusive. Each possible subset of 5 integers has the same probability of being chosen. These integers are called the winning numbers. A ticket is considered a winner if and only if it has a row which contains at least 3 winning numbers.

Alice will buy a single ticket. Each possible ticket has the same probability of being sold. Return the probability that she will buy a winning ticket.

Definition

Class:
LotteryPyaterochka
Method:
chanceToWin
Parameters:
int
Returns:
double
Method signature:
double chanceToWin(int N)
(be sure your method is public)

Notes

  • Your return value must have an absolute or relative error less than 1e-9.

Constraints

  • N will be between 1 and 100, inclusive.

Examples

  1. 1

    Returns: 1.0

    Any ticket contains just one line with some permutation of numbers 1, 2, 3, 4, 5. Ony one set of winning numbers is possible - {1, 2, 3, 4, 5}. So the only line of any ticket contains all 5 winning numbers, and therefore each ticket is a winner.

  2. 2

    Returns: 1.0

    For any set of winning numbers chosen, there's exactly one line in any ticket that contains at least 3 winning numbers.

  3. 3

    Returns: 0.5004995004995004

  4. 6

    Returns: 0.13161551092585574

  5. 100

    Returns: 4.7998099843704644E-4

  6. 99

    Returns: 4.897261613130418E-4

  7. 57

    Returns: 0.0014771963055972357

  8. 70

    Returns: 9.79512362113221E-4

  9. 4

    Returns: 0.2905056759545923

  10. 5

    Returns: 0.18831168831168824

  11. 7

    Returns: 0.09705451095394169

  12. 8

    Returns: 0.07447933763723237

  13. 9

    Returns: 0.05893879234775434

  14. 10

    Returns: 0.04779210481602446

  15. 11

    Returns: 0.039528728762913

  16. 12

    Returns: 0.03323475257401247

  17. 13

    Returns: 0.028331255823323506

  18. 14

    Returns: 0.024437218696103304

  19. 15

    Returns: 0.02129362625214449

  20. 16

    Returns: 0.0187194550952046

  21. 17

    Returns: 0.016585117084676294

  22. 18

    Returns: 0.014795877828954968

  23. 19

    Returns: 0.013281189283099104

  24. 20

    Returns: 0.011987644167320163

  25. 21

    Returns: 0.01087421266837838

  26. 22

    Returns: 0.009908954314662415

  27. 23

    Returns: 0.00906670527071086

  28. 24

    Returns: 0.00832742394264724

  29. 25

    Returns: 0.007674989188542127

  30. 26

    Returns: 0.007096314995509283

  31. 27

    Returns: 0.006580689867749947

  32. 28

    Returns: 0.006119278042572383

  33. 29

    Returns: 0.0057047387733632875

  34. 30

    Returns: 0.005330932792549046

  35. 31

    Returns: 0.004992693867686179

  36. 32

    Returns: 0.004685649464225554

  37. 33

    Returns: 0.0044060788129125054

  38. 34

    Returns: 0.004150799725544582

  39. 35

    Returns: 0.003917077692678836

  40. 36

    Returns: 0.003702552388144598

  41. 37

    Returns: 0.0035051778730478284

  42. 38

    Returns: 0.0033231736570587546

  43. 39

    Returns: 0.0031549844212801314

  44. 40

    Returns: 0.002999246694153426

  45. 41

    Returns: 0.0028547611418308044

  46. 42

    Returns: 0.002720469417499033

  47. 43

    Returns: 0.0025954347322278584

  48. 44

    Returns: 0.0024788254790646673

  49. 45

    Returns: 0.0023699013741218964

  50. 46

    Returns: 0.0022680016820733223

  51. 47

    Returns: 0.0021725351753470743

  52. 48

    Returns: 0.002082971541314377

  53. 49

    Returns: 0.0019988340036656686

  54. 50

    Returns: 0.0019196929657938045

  55. 51

    Returns: 0.001845160517557543

  56. 52

    Returns: 0.001774885673967205

  57. 53

    Returns: 0.0017085502364297962

  58. 54

    Returns: 0.0016458651852358154

  59. 55

    Returns: 0.0015865675267664305

  60. 56

    Returns: 0.0015304175310796172

  61. 58

    Returns: 0.0014267036589595454

  62. 59

    Returns: 0.0013787562160567951

  63. 60

    Returns: 0.0013331857510439364

  64. 61

    Returns: 0.0012898377099990143

  65. 62

    Returns: 0.0012485698989641828

  66. 63

    Returns: 0.0012092513165447788

  67. 64

    Returns: 0.0011717611131459912

  68. 65

    Returns: 0.0011359876613876154

  69. 66

    Returns: 0.0011018277243285389

  70. 67

    Returns: 0.0010691857099140811

  71. 68

    Returns: 0.0010379730015809387

  72. 69

    Returns: 0.0010081073562572295

  73. 71

    Returns: 9.521169493801175E-4

  74. 72

    Returns: 9.258549483834685E-4

  75. 73

    Returns: 9.006646896542007E-4

  76. 74

    Returns: 8.764886416005803E-4

  77. 75

    Returns: 8.532730817626101E-4

  78. 76

    Returns: 8.309677981382295E-4

  79. 77

    Returns: 8.095258174782204E-4

  80. 78

    Returns: 7.889031578023434E-4

  81. 79

    Returns: 7.69058602700162E-4

  82. 80

    Returns: 7.499534952523081E-4

  83. 81

    Returns: 7.315515496468652E-4

  84. 82

    Returns: 7.138186787755071E-4

  85. 83

    Returns: 6.967228362788474E-4

  86. 84

    Returns: 6.802338716734346E-4

  87. 85

    Returns: 6.643233973367226E-4

  88. 86

    Returns: 6.489646662536306E-4

  89. 87

    Returns: 6.341324595410416E-4

  90. 88

    Returns: 6.198029828665948E-4

  91. 89

    Returns: 6.059537709669546E-4

  92. 90

    Returns: 5.925635995497606E-4

  93. 91

    Returns: 5.796124039338543E-4

  94. 92

    Returns: 5.670812038451472E-4

  95. 93

    Returns: 5.549520338415766E-4

  96. 94

    Returns: 5.432078788907151E-4

  97. 95

    Returns: 5.318326146684995E-4

  98. 96

    Returns: 5.208109521877798E-4

  99. 97

    Returns: 5.10128386401491E-4

  100. 98

    Returns: 4.997711484577105E-4

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