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5. Fifth Prize Level: Match three numbers plus the Powerball (1 in 14,494.11 odds) Step 1: Calculate the number of ways in which 3 numbers can be chosen correctly out of 5 numbers drawn from 69 unique numbers. The formula is as follows: 5! ∗ (69 − 5)! = 5 ∗ 4 ∗ 3! ∗ 64! = 5 ∗ 4 ∗ 64 ∗ 63 ∗ 62! = 5 ∗ 64 ∗ 63 = 20,160 3!(5−3)! �(69−5)−(5−3)�!(5−3)! 3! 2! (64−2)! 2! 2 62!2∗1 This means that there are 20,160 different ways in which 3 numbers out of 5 numbers drawn from a field of 69 numbers can be chosen correctly. Thus, the chances are 20,160 in 11,238,513 of correctly choosing 3 out of 5 numbers in the first portion of PowerBall. Step 2: The chance of correctly choosing the Powerball is simply 1 in 26. Step 3: Determine the chances of choosing 3 out of 5 of 69 correctly and getting the Powerball correct by multiplying these figures together: 20,160 ∗ 1 = 20,160 = 1 or 1 chance in 14,494.11. 11,238,513 26 292,201,338 14,494.11 6. Sixth Prize Level: Match three numbers only (1 in 579.76 odds) Step 1: The chances of getting 3 numbers correct out of 5 numbers drawn from 69 unique numbers are 20,160 in 11,238,513 (see #5, Step 1, above.) Step 2: The chance of correctly choosing the Powerball is 1 in 26. Therefore, the chances of incorrectly choosing the Powerball are, conversely, 25 in 26. Step 3: Determine the chances of choosing 3 out of 5 of 69 correctly and getting the Powerball incorrect by multiplying these figures together: 20,160 ∗ 25 = 504,000 = 1 or 1 chance in 579.76. 11,238,513 26 292,201,338 579.76PDF Image | How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels
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