Please correct me if i'm wrong:
This is our travel map:
A.......
.........
.........
.........
.......B
In order to get from A to B we need to pass X-1 blocks (streets) plus Y-1 blocks (avenues); -1 because we start from a certain street and avenue and should not count them.
On every crossroad we can walk either DOWN or RIGHT, so our travel route will be something like DDDRDRDR, where D=X-1 times and R=Y-1 times.
We can do this in ((X-1)+(Y-1))!=(X+Y-2)! / (X-1)!(Y-1)! ways, soE ?
...
This is our travel map:
A.......
.........
.........
.........
.......B
In order to get from A to B we need to pass X-1 blocks (streets) plus Y-1 blocks (avenues); -1 because we start from a certain street and avenue and should not count them.
On every crossroad we can walk either DOWN or RIGHT, so our travel route will be something like DDDRDRDR, where D=X-1 times and R=Y-1 times.
We can do this in ((X-1)+(Y-1))!=(X+Y-2)! / (X-1)!(Y-1)! ways, soE ?
...
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