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3. Third Prize Level: Match four numbers plus the Powerball (1 in 913,129.18 odds) Step 1: Calculate the number of ways in which 4 numbers can be chosen correctly out of 5 numbers drawn from 69 unique numbers. The formula is as follows: 5! ∗ (69 − 5)! = 5 ∗ 4! ∗ 64! = 5 ∗ 64 ∗ 63! = 5 ∗ 64 = 320 4!(5−4)! �(69−5)−(5−4)�!(5−4)! 4! 1! (64−1)! 1! 1 63!1 This means that there are 320 different ways in which 4 numbers out of 5 numbers drawn from a field of 69 numbers can be chosen correctly. Thus, the chances are 320 in 11,238,513 of correctly choosing 4 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 4 out of 5 of 69 correctly and getting the Powerball correct by multiplying these figures together: 320 ∗ 1 = 320 = 1 or1chancein913,129.18. 11,238,513 26 292,201,338 913,129.18 4. Fourth Prize Level: Match four numbers only (1 in 36,525.17 odds) Step 1: The chances of getting 4 numbers correct out of 5 numbers drawn from 69 unique numbers are 320 in 11,238,513 (see #3, 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 4 out of 5 of 69 correctly and getting the Powerball incorrect by multiplying these figures together: 320 ∗ 25 = 8,000 = 1 or 1 chance in 36,525.17. 11,238,513 26 292,201,338 36,525.17PDF Image | How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels
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