I was just wondering if there is a method to approach the following question:

(there is a 3 by 2 grid, with x at the bottom left corner, and y at the top right corner)

Pat will walk from intersection x to y along a route that is confined to the square grid of four streets and three avenues shown in the preceding map. how many routes from x to y can pat take that have the minimum possible length?

Thank you!

Please post the entire text including answer choices. Often, the way in which the choices are presented dictates the most effective way to solve the problem!

Here is the solution: (I'm just wondering if there is another way to solve the problem - an easier way) Thank you!

In order to walk from intersection X to intersection Y by one of the routes of minimum possible length, Pat must travel only upward or rightward between the intersections on the map. Let U represent upward movements and R represent rightward movements. It takes 3 upward and 2 rightward movements to complete the route. The following 10 routes are possible:

UUURR
UURUR
UURRU
URUUR
URURU
URRUU
RRUUU
RUUUR
RUURU
RURUU

Answer is (C)

where:
A) 6
B) 8
C) 10
D) 14
E) 16

Thank you!

1. ) Let 5! be the number of possible movements Pat can make. 5*4*3*2*1 = 120

2.) Since we need the shortest route, from looking at the grid you can see that it will take 3 upward movements and 2 movements to the
right.

Following the combinatory method in the book it can be written as:
A B C D E
U U U R R

OR

3! * 2! = 12


Putting it all together you divide the first part by the second part:

5! / (3! * 2!) = 10

The OG's explanation is to write it all out? Yuck! The last Guest's method does indeed show a formulaic way to approach this.