Pre-Calculus

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I would like to know a formula to solve the number of combinations of 1 number from each of 5 sets of numbers (up to 8 numbers in each set), where combinations are only valid if the numbers chosen from each set is different from the other 4 numbers chosen.

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For example: [1 2 3], [1, 4, 6, 7], [3, 4], [7, 9, 10], [2, 4, 6, 7, 8] choose 1 number from each for a single combination

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