Counting states for Peg Solitaire 2^33 != Riemann Sum i = 1, n = 33 (nCi)?

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So I have this question that is finding all states (not possible states just states if this game didn't have rules) for a game of Peg Solitaire.

For those unaware of what it is: https://www.youtube.com/watch?v=Bt6GpGvUNeQ.

I understand that 2^33 will get all states because there are 33 slots in the game and they can either be filled with a peg or empty (hence where the 2 comes from because 2 states), but is that not the same as getting the Riemann sum of the combinations of empty slots on the board?