Calculating Routes on a Grid: Using Combinations and Pascal's Triangle

[SeththeBaller]

1. The streets of a city are laid out in a rectangular gird, as shown below

a) Use combinations to find the number of routes through the grid that lead from point A to point B by only traveling north or east. Show your calculations

b) How many of these routes pass through intersections C



2. Alright, so I've solved similar questions before. I get to P(66,6)/6! only to get some absurd answer. I understand that from point A to point B there is a distance of 66 blocks-11 east, 6 north. Somehow I believe that the exponential answer that comes from this is not what my professor expects.

I was wondering if I could have help with this please and thank you :D

 

[tal444]

How did you get 66 blocks? No matter how you travel, the most you could possibly get is 17 (11 east + 6 north). Multiplying gives you the area, not the distance.

 

[SeththeBaller]

Whoops, lmao, sorry long day, that makes so much sense, I know what to do from here lol

 

[tal444]

Np, I know the feeling, gl :P