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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems

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THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems ( the-mathematics-lottery-odds-combinations-systems )

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.............. missing part ................... Example of how to use the table: In a 7/47 matrix, we played a 15-number compound line. What is the number of simple lines containing exactly 5 winning numbers, if exactly 6 winning numbers from the played 15 occurred in the draw? We follow the intersection of row r = 15 with the column corresponding to (k = 6; k – i = 5) and find 216 simple lines with exactly 5 winning numbers. If in addition we want to find the probability of having 6 winning numbers among the played 15, we consult the table 7/47 in the previous section devoted to the probabilities of winning with compound lines (for r = 15 and w = 5) and find 0.023683, that is 2.3683%. The general formula and the tables of this section cover all possible values of the number of winning numbers (k) from a compound line. In particular, among these values of k there are also the thresholds of the winning categories n , n ,, n , for any lottery 12q matrix. For most lotteries, we have ni−1 = ni +1, for every i = 2, ..., q (passing to the next higher threshold of the winning category is done by increasing the current one with 1). .............. missing part ................... 47

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