I don't know if the fact that the lottery is in 12 states affects the problem, so I'm just going to assume that it does not.
I'll also assume that the 5 numbers could be equal. If that is so, then the probability for 5 numbers between 1 and 56 is \(56^5\), times the probability for the single number between 1 and 46 which is 46. Multiplying gives \(56^5 \cdot 46.\)
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