Exercise 10.

For each of the following, find the number of shortest lattice paths from \((0,0)\) to \((8,8)\) which:

  1. pass through the point \((2,3)\text{.}\)

  2. avoid (do not pass through) the point \((7,5)\text{.}\)

  3. either pass through \((2,3)\) or \((5,7)\) (or both).

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