In a city where all streets run east-to-west, all avenues run north-to

Question

https://gmatclub.com/forum/download/file.php?id=25954 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 Street_Map.png

Lucky2783 · Accepted Answer

She choose a route which allows her to walk fewest number of blocks 
there are 2 blocks she will cross towards east moves represented by E,E and there will be 5 blocks she will cross towards south represented by S,S,S,S,S

total number of ways  \frac{7!}{5!2!}

there are 4 ways she can cross 2 blocks on av.1 as shown in attached image.

4/21 is Answer .

in order to reach from black dot to blue dot she has to make 1 E and 3 S moves .. total 4!/3! = 4Ways . now from Blue dot to Maroon dot there is only 1 way . so there are only 4 ways .

A

Bunuel · Answer

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bumpbot · Answer

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In a city where all streets run east-to-west, all avenues run north-to

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In a city where all streets run east-to-west, all avenues run north-to

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