Math CentralQuandaries & Queries


Question from Lee:

A friend and I are trying to calculate the odds of choosing the winning numbers in the 3-ball lottery (3-digits 0-9). We realize that there are 720 Permutations and 120 possible Combinations of said lottery, but we're having trouble figuring how to determine the "odds" or probability of winning (1) when order matters, and (2) when it doesn't. Please help!

Hi Lee,

You have done almost all the work. If order does matter and you count permutations then there are 720. Of the 720 possibilities there is only 1 winner so the probability that you win is 1/720. Similarly if order does not matter then there are 120 possibilities so the probability you win is 1/120.

I hope this helps,

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