Hi All,
We're told that X and Y represent locations in a district of a certain city where the streets form a rectangular grid. We're asked to travel ONLY North OR EAST along the streets from X to Y. We're asked for the number of different paths that are possible. This question is a variation on the Combination Formula.
To start, since we can ONLY travel North OR East, we will eventually have to travel 3 streets "up" and 5 streets "to the right" (in some order). That ultimately means that we will have 8 total "moves." Sometimes we'll be able to choose to go North or East, but sometimes we'll have no choice (we'll only be able to North or only be able to go East). The order of the "up" moves and "to the right" moves does NOT matter though, as long as we get from X to Y. Since the order does not matter, that's a hint to use the Combination Formula:
N!/(K!)(N-K)!
Here, N = 8 (since there are 8 total moves) and we can make the K equal either 3 or 5 (for the 3 "up" moves or 5 "to the right" moves). Either calculation will end in the same value...
8!/(3!)(5!) or 8!/(5!)(3!)
This will give us (8)(7)(6)/(3)(2)(1) = (8)(7)/1 = 56 possible ways to get from X to Y.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
