Proof the formula "how many ways to walk"
Here is a simple proof:
Walking from (0, 0) to (5, 4), one way is as shown in the picture.
It is the same solution as to the question: how many ways are there to arrange
b a b b a a b a b
in a row?
Similarly we can get the ways to walk from (0, 0) to (m, n).
