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Powerball is a game of combinations of 59 things (balls) taken 5 at a time, plus the combinations of 39 things taken 1 at a time.

The combinations of N things taken P at a time is (N! - P!) / P!

For the first part, this is 5,006,386. For the second part, this is 39. The total number of combinations is the product of the two, or 195,249,054.

The Australian version is similar, but uses 45 things in both parts, so the total combinations is 1,221,759 times 45, or 54,979,155.

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