Feynman Checkerboard!

Richard P Feynman starts his journey from $$O=(0,0)$$ towards $$A=(10,6).$$ He can only go in the $$+x$$ and $$+y$$ directions along the lattice, and he must turn exactly 7 times. An example path is shown above, with the yellow dots indicating turns.

How many ways can Feynman travel from $$O$$ to $$A$$ in this way?

Bonus: Consider the general case, traveling from $$(0,0)$$ to $$(p,q)$$ with exactly $$r$$ turns.

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