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To win the jackpot there are 5,006,386 combinations for the five numbers x 35 powerball choices, so there are 175,223,510 combinations for picking the jackpot combination.
There is 1 combination of all ten numbers, 10 combinations of one number and of nine numbers, 45 combinations of two or eight numbers, 120 combinations of three or seven numbers, 210 combinations of four or six numbers and 252 combinations of five numbers. That is 1023 = 210 - 1 in total.
There are 125970 combinations and I am not stupid enough to try and list them!
There are a huge number of combinations of 5 numbers when using the numbers 0 through 10. There are 10 to the 5th power combinations of these numbers.