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In the figure above, \(X\) and \(Y\) represent locations in a district of a certain city where the streets form a rectan

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by Gmat_mission » Sun Mar 07, 2021 4:01 pm

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2019-09-21_1421.png
In the figure above, \(X\) and \(Y\) represent locations in a district of a certain city where the streets form a rectangular grid. In traveling only north or east along the streets from \(X\) to \(Y,\) how many different paths are possible?

A. 720
B. 512
C. 336
D. 256
E. 56

Answer: E

Source: Official Guide
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Re: In the figure above, \(X\) and \(Y\) represent locations in a district of a certain city where the streets form a re

by regor60 » Wed Mar 10, 2021 12:59 pm
To get from X to Y 5 steps to the right and 3 steps up need to be taken and there are many paths.

The problem is simplified in that no steps to the left or down are permitted.

One can therefore see that the 5 steps to the right can be shown as RRRRR and the 3 up as UUU.

As a group these 8 steps can be arranged 8! ways. However, this treats each R and U as unique where of course each R and U is identical to other Rs and Us.

To find the unique paths one needs to divide 8! by 5! and 3!.

8!/5!3! = 56, E
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