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From the article: Gearbox has not given an exact figure, though Randy Pitchford has stated that the number greatly exceeds the original game’s total and “There are enough where it doesn’t matter. It really doesn’t matter.”
The game has too many combinations to count, but as for the “named” guns (such as quest items, or like Miss Moxxie’s Good Touch kind of thing) there is about 130. (I’m estimating from the amount of quests that rewards you with a named gun)