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How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels: PowerBall numbers are drawn from two sets of numbers. Five numbers are drawn from one set of 69 numbered white balls and one Powerball number is drawn from a second set of 26 numbered red balls. The odds of winning PowerBall are calculated by combining the odds for both sets of numbers for all prize levels. The first, third, fifth, and seventh through ninth prize level odds are determined by the chances of choosing a given number of white balls correctly as well as the red Powerball. The second, fourth and sixth prize level odds are determined by the chances of choosing a given number of white balls correctly and the red Powerball incorrectly. Since the order of the items chosen is irrelevant, the applicable probability rule is the formula to determine combinations. Before calculating the odds for the different prize levels, calculate the total number of combinations possible for each portion of the PowerBall draw. A. Calculate how many combinations of 5 numbers can be drawn from 69 unique numbers: The formula is as follows: 69! = 69 ∗ 68 ∗ 67 ∗ 66 ∗ 65 ∗ 64! = 69 ∗ 68 ∗ 67 ∗ 66 ∗ 65 = 1,348,621,560 = 11,238,513 5! (69 − 5)! 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 ∗ 64! 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 120 where!indicatesafactorial,i.e.,n! = n ∗ (n−1) ∗ (n−2) ∗...∗ 2 ∗ 1 Thus, there are 11,238,513 different ways in which 5 numbers can be chosen from a total of 69 unique numbers. B. Calculate how many combinations of 1 number can be drawn from 26 unique numbers: 26! = 26 ∗ 25! = 26 1! (26 − 1)! 1 ∗ 25! Thus, there are 26 different ways 1 number can be chosen from a total of 26 unique numbers.PDF Image | How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels
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