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9. Ninth Prize Level: Match the Powerball only (1 in 38.32 odds) Step 1: Calculate the number of ways in which no numbers are chosen correctly out of 5 numbers drawn from 69 unique numbers. The formula is as follows: 5! ∗ 64! = 64 ∗ 63 ∗ 62 ∗ 61 ∗ 60 ∗ 59! = 64 ∗ 63 ∗ 62 ∗ 61 ∗ 60 = 7,624,512 5! ∗ (69 − 5)! = 0!(5−0)! �(69−5)−(5−0)�!(5−0)! 1∗5! (64−5)! 5! 59!5∗4∗3∗2∗1 120 (𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁: 0! = 1) This means that there are 7,624,512 different ways in which no numbers out of 5 numbers drawn from a field of 69 numbers are chosen correctly. Thus, the chances are 7,624,512 in 11,238,513 of correctly choosing 0 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 0 out of 5 of 69 correctly and getting the Powerball correct by multiplying these figures together: 7,624,512 ∗ 1 = 7,624,512 = 1 or 1 chance in 38.32. 11,238,513 26 292,201,338 38.32PDF Image | How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels
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