Stanley's Saga

The protagonist of this story, Stanley, is standing peacefully at coordinates \( (0, \space 0) \) without any concern in his life whatsoever.

Now, Stanley will move at coordinates \( (3, \space 4) \).

If Stanley only goes either up, or right, or up-right (corresponding vectors in their respective order: \( \vec{u}(0, \space 1) \), \( \vec{r}(1, \space 0) \) , \( \vec{ur}(1, \space 1) \)), on how many ways can Stanley accomplish this tremendous stunt?

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