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Number Combinations The number combinations are the structural units of the lotto game, and their unfolding and generation represent the “engine” of every number lottery, for both the technical process of the game and placing the bets (creating the playing tickets) by the players. The number combinations show up within the draws, being randomly generated by the shuffling and drawing device, as well as in lines played on the playing tickets, these latter being chosen by players from all possible allowed combinations. The sizes of the number combinations involved in the lotto game, in intermediary moments of its process or as the final result of the drawing, vary from 1 up to the total number of numbers of a draw (previously denoted by n). A drawing is complete when all n numbers of a draw have been extracted from all m that the urn contains. This draw represents an n-size combination of numbers, and the set of combinations possible to be drawn is the set of all combinations of the m numbers taken each n, which contains Cmn elements. By using formula (F10) we can calculate the number of all combinations possible to be drawn for any lottery matrix. In the table below are noted these numbers for a few of the most popular lottery matrices: n m 32 40 44 45 48 49 55 90 456 7 35960 201376 91390 658008 135751 1086008 148995 1221759 194580 1712304 211876 1906884 341055 3478761 2555190 43949268 906192 3365856 3838380 18643560 7059052 38320568 8145060 45379620 12271512 73629072 13983816 85900584 28989675 202927725 622614630 7471375560 20PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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