How many configurations of two pairs can there be in a single poker hand?

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For the sake of simplicity, let's say the poker hand is sorted. So the hand is 2 2 3 3 4. I'm coming up with a poker hand can have four possible configurations where it has two pairs. Suppose the hand looks like 1 1 _ _ _, meaning this hand can have two more configurations: 11 22 3 and 11 2 33. This leaves us with the last configuration of: 1 22 33. If the first card doesn't have a pair, that means only the last four cards can have two pairs. Is this thinking incorrect?