Number of ways to go to the opposite corner.

[ssd]

# of ways to go to the opposite corner.

Suppose m+1 parallel (laid N-S)roads cross n+1 parallel (laid E-W) roads. In how many different ways one can move from North- East corner (of crossing) to South- West corner heading either West or South? What the simplest / attractive way (explanation) to make students of age 17yr understand while teaching in class. I observed, students really do not get the logic.

 

[Hurkyl]

The usual way to do this is to write paths as words in the letters "S" and "W", and count how many of those words correspond to a path from one corner to another, right?

I imagine the best way would be to make them understand the bijection. Exercises converting from words to paths and back. Have them think about which words correspond to a path from corner to corner.

 

[ssd]

Nice.