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Observe that the number of all possible combinations for the entire draw increases with both m and n, when the other variable is fixed. For the 6/49 lottery matrix, this number is 13,983,816; for 6/44 matrix it is 7,059,052; and for 5/55 it is 3,478,761. Using formula (F10), we can also calculate numbers of possible combinations for intermediary moments of a drawing, for example for the first drawn numbers. If we choose n ' < n , the number of possible combinations for the first n' numbers of the draw is Cmn' . Examples: In the 6/49 matrix, the number of possible combinations for the first 3 drawn numbers is C3 = 47⋅48⋅49 =18424. 49 2⋅3 In the 5/55 matrix, the number of possible combinations for the first 4 drawn numbers is C4 = 52⋅53⋅54⋅55 = 341055. 55 2⋅3⋅4 We can also calculate numbers of possible combinations for the last numbers of the draw, at specific moments of the drawing. In this case, we shall take into account the number of the numbers already drawn. Still staying with n ' ( n ' < n ) denoting the number of the numbers drawn at a certain moment, the number of possible combinations for the rest of the numbers following to be drawn is .............. missing part ................... 21PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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