Solution
Grid Paths
Show the problem again
How many paths are there from the bottom-left corner to the top-right corner of an 8 × 8 grid of unit squares, moving only right or up along grid lines?
Worked solution
The answer is 12,870. Every path is a sequence of 8 right-moves and 8 up-moves in some order, 16 steps total. Choosing which 8 of the 16 steps go right determines the path: C(16, 8) = 12,870.
Source: Standard lattice-path counting exercise from introductory combinatorics texts. Statement written for AxiomIQ.