How to calculate the total number of combinations of dependent variables with non-uniform distribution?

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How to calculate the total number of combinations of dependent variables with non-uniform distribution? for example, if I have 3 variable A, B, and C; each of them can have N different discrete states and with some correlation < 1. I have the probability distribution of each variable too. How can I calculate the exact number of combinations they can generate? Thank you!

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Counting only states with a probability greater than zero, the total number of combinations is calculated without regard for the underlying distribution.