BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1622
Joined: Thu Mar 01, 2018 7:22 am
Followed by:2 members

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

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

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
Top
Post new topic Post Reply
• Page 1 of 1