Problem Solving

In a city where all streets run east-to-west, all avenues run north-to-south, and all intersections are right angles as shown below, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the fewest number of blocks, what is the probability that she walks exactly two blocks on 1st Avenue?

a) 1/21
b) 1/7
c) 4/21
d) 10/21
e) 12/21


OA C

Source: Veritas Prep

5 steps down and 2 to the right are required to make the trip.

The 5 steps down can be allocated to the 3 avenues

7!/5!2! = 21 ways

Since 2 steps down are allocated to avenue 1 in the question, this leaves 3 steps to be allocated to the other 2 avenues, which can be done

4!/3! = 4 ways

Answer [spoiler]4/21, C[/spoiler]