Powerball Odds: A Comprehensive Guide to Calculating Your Chances

In Powerball, a lottery game played in dozens of states across the United States, you have to correctly match the numbers on five white balls, no matter the order, and one red ball (the "Powerball"). To calculate the odds, you need to know a math operation called "factorial." Factorial is symbolized by an "!." When you take the factorial of a number, you multiple that number by each number below it, down to one. For example, 4! equals "4 x 3 x 2 x 1," or 24. After you calculate your odds of winning, you might think twice before playing next time.

Step 1

Calculate the factorial of the number of white balls drawn. For example, if Powerball uses 59 white balls, calculate the factorial of 59 to get 138,683,118,545,690,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

Step 2

Calculate the factorial of the number of white balls minus the number of white balls drawn. For example, if there are 59 white balls and five are drawn, calculate 55! to get 12,696,403,353,658,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

Step 3

Calculate the factorial of the number of white balls drawn. In this example, calculate 5! to get 120.

Step 4

Multiply the factorial of the number of white balls minus the number of white balls drawn by the factorial of the number of white balls drawn. In this example, multiply 12,696,403,353,658,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 by 120 to get 230,843,697,339,241,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

Step 5

Divide the factorial of the number of white balls (the step 1 result) by the product of the factorial of the number of white balls minus the number drawn times the factorial of the number of white balls drawn (the step 4 result) to calculate the number of possible combinations for the white balls drawn. In this example, divide 138,683,118,545,690,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 by 230,843,697,339,241,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 to get 5,006,386.

Step 6

Multiply the number of combinations for the white balls by the number of red balls to find the odds of winning Powerball. Assuming there are 35 red balls, multiply 5,006,386 by 35 to get 175,223,510, meaning that you have a 1 in 175,223,510 chance of winning.