How to represent a problem of choosing one permutation over x different subsets of combinations?

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I'm writing a computer program and I have problems understanding how to iterate this problem:

  • 3 independent sets of numbers where I need to choose two out of three. That falls under simple category of combinations without repetition. So if I have numbers 1,2,3 and I choose two, I have only three unique combinations for that set.

  • Out of that 3 given sets, I need to create a "globally" unique combination. Using the 3 {1,2,3} sets, one unique combination would be {{1,2}, {1,3}, {1,3}}, antoher would be {{1,3}, {2,3}, {2,2}}

Can you point out a formula I could use for this?