Calculations for item eight of American Scientific page


TOBEORNOTTOBE

The number of possible combinations for letters of the alphabet

Numbers followed by E+… means add noughts to the end until the number of figures after the decimal point is the same as the number after the plus sign, then remove the decimal point. So the greater the number after ‘E’, the larger the amount.

 LETTERS

NUMBER OF DIFFERENT COMBINATIONS


26

676

17576

456976

11881376

308915776

8031810176

2.08827E+11

5.4295E+12

1.41167E+14

3.67034E+15

9.5429E+16

2.48115E+18


26 x 1 =

26 x 26 =

26 x 676 =

26 x 17576  =

26 x 456976  =

26 x 11881376  =

26 x 308915776  =

26 x 8031810176  =

26 x 2.08827E+11  =

26 x 5.4295E+12  =

26 x 1.41167E+14  =

26 x 3.67034E+15  =

26 x 9.5429E+16  =


1

2

3

4

5

6

7

8

9

10

11

12

13

One different combination per second

  2.48115E+18 (seconds)

  2.48115E+18 / 60 = 4.13525E+16 (minutes)

  4.13525E+16 / 60 = 6.89209E+14 (hours)

  6.89209E+14 / 24 = 2.8717E+13 (days)

  2.8717E+13 / 365.25 = 78,622,990,126 (years)



Nucleotides

The number of possible combinations for the four different letters of DNA (A, C, G, T)

 LETTERS

NUMBER OF DIFFERENT COMBINATIONS

 LETTERS

NUMBER OF DIFFERENT COMBINATIONS

4

16

64

256

1024

4096

16384

65536

262144

1048576

4194304

16777216

67108864

268435456

1073741824

4294967296

17179869184

68719476736

2.74878E+11

1.09951E+12

4.39805E+12

1.75922E+13

7.03687E+13

2.81475E+14

1.1259E+15

4 x 1 =

4 x 4 =

4 x 16 =

4 x 64 =

4 x 256 =

4 x 1024 =

4 x 4096 =

4 x 16384 =

4 x 65536 =

4 x 262144 =

4 x 1048576 =

4 x 4194304 =

4 x 16777216 =

4 x 67108864 =

4 x 268435456 =

4 x 1073741824 =

4 x 4294967296 =

4 x 17179869184 =

4 x 68719476736 =

4 x 2.74878E+11 =

4 x 1.09951E+12 =

4 x 4.39805E+12 =

4 x 1.75922E+13 =

4 x 7.03687E+13 =

4 x 2.81475E+14 =


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

4.5036E+15

1.80144E+16

7.20576E+16

2.8823E+17

1.15292E+18

4.61169E+18

1.84467E+19

7.3787E+19

2.95148E+20

1.18059E+21

4.72237E+21

1.88895E+22

7.55579E+22

3.02231E+23

1.20893E+24

4.8357E+24

1.93428E+25

7.73713E+25

3.09485E+26

1.23794E+27

4.95176E+27

1.9807E+28

7.92282E+28

3.16913E+29

1.26765E+30

4 x 1.1259E+15 =

4 x 4.5036E+15 =

4 x 1.80144E+16 =

4 x 7.20576E+16 =

4 x 2.8823E+17 =

4 x 1.15292E+18 =

4 x 4.61169E+18 =

4 x 1.84467E+19 =

4 x 7.3787E+19 =

4 x 2.95148E+20 =

4 x 1.18059E+21 =

4 x 4.72237E+21 =

4 x 1.88895E+22 =

4 x 7.55579E+22 =

4 x 3.02231E+23 =

4 x 1.20893E+24 =

4 x 4.8357E+24 =

4 x 1.93428E+25 =

4 x 7.73713E+25 =

4 x 3.09485E+26 =

4 x 1.23794E+27 =

4 x 4.95176E+27 =

4 x 1.9807E+28 =

4 x 7.92282E+28 =

4 x 3.16913E+29 =


26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

5.0706E+30

2.02824E+31

8.11296E+31

3.24519E+32

1.29807E+33

5.1923E+33

2.07692E+34

8.30767E+34

3.32307E+35

1.32923E+36

5.31691E+36

2.12676E+37

8.50706E+37

3.40282E+38

1.36113E+39

5.44452E+39

2.17781E+40

8.71123E+40

3.48449E+41

1.3938E+42

5.57519E+42

2.23007E+43

8.9203E+43

3.56812E+44

1.42725E+45

4 x 1.26765E+30 =

4 x 5.0706E+30 =

4 x 2.02824E+31 =

4 x 8.11296E+31 =

4 x 3.24519E+32 =

4 x 1.29807E+33 =

4 x 5.1923E+33 =

4 x 2.07692E+34 =

4 x 8.30767E+34 =

4 x 3.32307E+35 =

4 x 1.32923E+36 =

4 x 5.31691E+36 =

4 x 2.12676E+37 =

4 x 8.50706E+37 =

4 x 3.40282E+38 =

4 x 1.36113E+39 =

4 x 5.44452E+39 =

4 x 2.17781E+40 =

4 x 8.71123E+40 =

4 x 3.48449E+41 =

4 x 1.3938E+42 =

4 x 5.57519E+42 =

4 x 2.23007E+43 =

4 x 8.9203E+43 =

4 x 3.56812E+44 =


51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

5.70899E+45

2.2836E+46

9.13439E+46

3.65375E+47

1.4615E+48

5.84601E+48

2.3384E+49

9.35361E+49

3.74144E+50

1.49658E+51

5.98631E+51

2.39452E+52

9.5781E+52

3.83124E+53

1.5325E+54

6.12998E+54

2.45199E+55

9.80797E+55

3.92319E+56

1.56928E+57

6.2771E+57

2.51084E+58

1.00434E+59

4.01735E+59

1.60694E+60

4 x 1.42725E+45 =

4 x 5.70899E+45 =

4 x 2.2836E+46 =

4 x 9.13439E+46 =

4 x 3.65375E+47 =

4 x 1.4615E+48 =

4 x 5.84601E+48 =

4 x 2.3384E+49 =

4 x 9.35361E+49 =

4 x 3.74144E+50 =

4 x 1.49658E+51 =

4 x 5.98631E+51 =

4 x 2.39452E+52 =

4 x 9.5781E+52 =

4 x 3.83124E+53 =

4 x 1.5325E+54 =

4 x 6.12998E+54 =

4 x 2.45199E+55 =

4 x 9.80797E+55 =

4 x 3.92319E+56 =

4 x 1.56928E+57 =

4 x 6.2771E+57 =

4 x 2.51084E+58 =

4 x 1.00434E+59 =

4 x 4.01735E+59 =


76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

If there are 10 possibilities in 100, this is the same as 1 possibility in 10.
If there are 100 possibilities in 1,000, this is the same as 10 possibilities in 100, which is the same as 1 possibility in 10. Therefore if you remove the same number of zeros from both figures, the odds remain the same. So if there are one billion valid sequences, then since there are nine zeros in one billion, if you remove nine zeros from the number of possibilities, then it tells you the odds against finding one.

1.60694E+60 minus nine zeros = 1.60694E+51

 So 1,000,000,000 in 1.60694E+60 is the same as 1 in 1.60694E+51


With 1.60694E+60 possible combinations, then trying one billion every second takes the following amount of time:

  1.60694E+60 / 1,000,000,000 = 1.60694E+51 (seconds)

  1.60694E+51 / 60 = 2.67823E+49 (minutes)

  2.67823E+49 / 60 = 4.46372E+47 (hours)

  4.46372E+47 / 24 = 1.85988E+46 (days)

  1.85988E+46 / 365.25 = 5.09208E+43 (years)

The odds against winning the UK lottery jackpot with the same numbers in consecutive draws, with the reported odds against winning it once reported by the http://playlotto.org.uk/lottery/uklottery_odds.html
as 1 in 45,057,474

Two draws: 45,057,474 x 45,057,474 = 2.03018E+15

Three draws: 45,057,474 x 2.03018E+15 = 9.14746E+22

Four draws: 45,057,474 x 9.14746E+22 = 4.12161E+30

Five draws: 45,057,474 x 4.12161E+30 = 1.8571E+38

Six draws: 45,057,474 x 1.8571E+38 = 8.3676E+45

(Compared to the odds against finding a viable sequence of 100 nucleotides with one billion viable sequences = 1.60694E+51)

Seven draws: 45,057,474 x 8.3676E+45 = 3.77023E+53