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7. Seventh Prize Level: Match two numbers plus the Powerball (1 in 701.33 odds) Step 1: Calculate the number of ways in which 2 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 ∗ 61! = 5 ∗ 64 ∗ 63 ∗ 62 = 416,640 2!(5−2)! �(69−5)−(5−2)�!(5−2)! 2! 3! (64−3)! 3! 2 61!3∗2∗1 3 This means that there are 416,640 different ways in which 2 numbers out of 5 numbers drawn from a field of 69 numbers can be chosen correctly. Thus, the chances are 416,640 in 11,238,513 of correctly choosing 2 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 2 out of 5 of 69 correctly and getting the Powerball correct by multiplying these figures together: 416,640 ∗ 1 = 416,640 = 1 or 1 chance in 701.33. 11,238,513 26 292,201,338 701.33 8. Eighth Prize Level: Match one number plus the Powerball (1 in 91.98 odds) Step 1: Calculate the number of ways in which 1 number 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 ∗ 62 ∗ 61 ∗ 60! = 5 ∗ 64 ∗ 63 ∗ 62 ∗ 61 = 3,176,880 1!(5−1)! �(69−5)−(5−1)�!(5−1)! 1! 4! (64−4)! 4! 1 60!4∗3∗2∗1 24 This means that there are 3,176,880 different ways in which 1 number out of 5 numbers drawn from a field of 69 numbers can be chosen correctly. Thus, the chances are 3,176,880 in 11,238,513 of correctly choosing 1 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 1 out of 5 of 69 correctly and getting the Powerball correct by multiplying these figures together: 3,176,880 ∗ 1 = 3,176,880 = 1 or 1 chance in 91.98. 11,238,513 26 292,201,338 91.98PDF Image | How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels
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