By a little investigation, any one may discover that his chance for drawing a prize, even of a trifling amount, is extremely small. By the following method any one may ascertain the number of combinations which any given number will produce, as in the present case, 78 x 77 x 76 = 456456 / 6 = 76076, the number of combinations of three numbers each; the 78 multiplied by 77, and the product by 76, and that product divided by 6 gives the number of combinations of three numbers each, which the numbers from 1 to 78 will produce, no two combinations containing the same three numbers.
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--------+ | #205# | #206# | #207# | #208# | #209# | #210# | +--------+----------+----------+---------+-----------+------
---+ | 5 | 6 | 7 | 8 | 9 | 10 | +--------+----------+----------+---------+-----------+------
---+ | 1 12 23| 1 13 25 | 1 14 27 | 1 15 29| 1 16 31 | 1 17 33| | 2 13 24| 2 14 26 | 2 15 28 | 2 16 39| 2 17 32 | 2 18 34| | 3 14 25| 3 15 27 | 3 16 29 | 3 17 31| 3 18 33 | 3 19 35| | 4 15 26| 4 16 28 | 4 17 30 | 4 18 32| 4 19 34 | 4 20 36| | 5 16 27| 5 17 29 | 5 18 31 | 5 19 33| 5 20 35 | 5 21 37| | 6 17 28| 6 18 30 | 6 19 32 | 6 20 34| 6 21 36 | 6 22 38| | 7 18 29| 7 19 31 | 7 20 34 | 7 21 35| 7 22 37 | 7 23 39| | 8 19 30| 8 20 32 | 8 21 33 | 8 22 36| 8 23 38 | 8 24 40| | 9 20 31| 9 21 33 | 9 22 35 | 9 23 37| 9 24 39 | 9 25 41| |10 21 32| 10 22 34 | 10 23 36 | 10 24 38| 10 25 40 | 10 26 42| |11 22 33| 11 23 35 | 11 24 37 | 11 25 39| 11 26 41 | 11 27 43| |34 45 56| 12 24 36 | 12 25 38 | 12 26 40| 12 27 42 | 12 28 44| |35 46 57| 37 49 61 | 13 26 39 | 13 27 41| 13 28 43 | 13 29 45| |36 47 58| 38 50 62 | 40 53 66 | 14 28 42| 14 29 44 | 14 30 46| |37 48 59| 39 51 63 | 41 54 67 | 43 55 67| 15 30 45 | 15 31 47| |38 49 60| 40 52 64 | 42 55 68 | 44 56 68| 46 57 68 | 16 32 48| |39 50 61| 41 53 65 | 43 56 69 | 45 57 69| 47 58 69 | 49 59 69| |40 51 62| 42 54 66 | 44 57 70 | 46 58 70| 48 59 70 | 50 60 70| |41 52 63| 43 55 67 | 45 58 71 | 47 59 71| 49 60 71 | 51 61 71| |42 53 64| 44 56 68 | 46 59 72 | 48 60 72| 50 61 72 | 52 62 72| |43 54 65| 44 55 66 | 45 47 73 | 49 61 73| 51 62 73 | 53 63 73| |44 55 66| 46 58 70 | 48 61 74 | 50 62 74| 52 63 74 | 54 64 74| |67 71 76| 47 59 72 | 49 62 75 | 51 63 75| 53 64 75 | 55 65 75| |68 72 75| 48 60 71 | 50 63 76 | 52 64 76| 54 65 76 | 56 66 76| |69 73 78| 73 75 77 | 51 64 77 | 53 65 77| 55 66 77 | 57 67 77| |70 74 77| 74 76 78 | 52 65 78 | 54 66 78| 66 67 78 | 58 68 78| +--------+----------+----------+---------+-----------+------
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+--------+----------+----------+---------+-----------+-
--------+ | #296# | #297# | #298# | #299# | #300# | #301# | +--------+----------+----------+---------+-----------+------
---+ | 11 | 12 | 13 | 14 | 15 | 22 | +--------+----------+----------+---------+-----------+------
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