How to select specific item from cartesian product without calculating every other item

The number of possible combinations ist given by

N = size(A) * size(B) * size(C)

and you can index all items by an index i ranging from 0 to N (exclusive) via

c(i) = [A[i_a], B[i_b], C[i_c]]

where

i_a = i/(size(B)*size(C)) 
i_b = (i/size(C)) mod size(B)
i_c = i mod size(C)

(all sets are assumed to be indexable starting wih zero, / is integer division).

In order to get your example you may shift the index by 1.

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