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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 [#permalink]

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New post 17 Mar 2015, 11:26
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Question Stats:

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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
[Reveal] Spoiler: OA

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Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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ynaikavde wrote:
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



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Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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New post 10 Apr 2015, 08:18
Bunuel, could you please explain how do we deal with the restriction ? (Only two blocks on 1st avenue).

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In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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ynaikavde wrote:
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



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 .


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Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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New post 10 Apr 2015, 11:40
Thank you Lucky2783 for the detailed explanation.

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Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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New post 07 Oct 2017, 06:21
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Re: In a city where all streets run east-to-west, all avenues run north-to   [#permalink] 07 Oct 2017, 06:21
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