Cookie?

Tia bakes \(35\) cookies and arranges them in a \(5\times7\) grid. However one cookie is poisoned and Tia puts the cookie at the bottom left corner of the grid. Two friends play a game by eating the cookies by alternating turns. When it is someone's turn, they pick any cookie that is still on the board and eat the cookies that are above or to the right of the cookie they just ate. How many possible positions are possible in this game? (Problem Inspired by AoPS)

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