I was studying about permutations and combinations, and I got a sense that...
A. We do cross products when the order matters (or each decision is different) and we can reuse each choice every time, as in boolean logical functions: We have 4 decisions (TT, TF, FT, FF), and 2 choices (T, F)... so 2 x 2 x 2 x 2.
B. We do permutations when the order matters, but we can't reuse choices. As in ranking members in a set. Therefore, we use factorials.
C. For combinations, the order doesn't matter, and we can't reuse choices.
Is this intuition sensible?
P.S. Are there cases where the order doesn't matter, but we can reuse choices? I can't think of one.