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I have a different view. If I understand well. We have to go from top-left to bottom-right. We have two types of step: R(ight), D(own).
(m-1) -> R
(n-1) -> D
So just have to count the Permutations of two type of steps (patterns or ways).
The problem if I am right hard to calculate. If I am wrong please let me know!
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Matrix Tracing
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I have a different view. If I understand well. We have to go from top-left to bottom-right. We have two types of step: R(ight), D(own). (m-1) -> R (n-1) -> D
So just have to count the Permutations of two type of steps (patterns or ways). The problem if I am right hard to calculate. If I am wrong please let me know!