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GMATT73
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Imagine a 3X2 grid as such with X in the bottom left hand 10 Nov 2005, 22:24
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Imagine a 3X2 grid as such with X in the bottom left hand corner and Y in the top right hand corner: How many possible ways can a person walk from X to Y in 5 steps (horizontal or vertical only)? The OG just reccommends visually counting all 10 ways, but surely there must be a faster way?

l----l----l
l----l----l
l----l----l



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Imagine a 3X2 grid as such with X in the bottom left hand 10 Nov 2005, 23:35
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let x = the path along the X axis and Y the path along the y axis


the path can be
XXXYY
XXYYX
XXYXY
XYXXY
XYXYX
XYYXX
YXXYX
YXXXY
YXYXX
YYXXX


SO ALL TOGETHER THERE ARE 10 POSSIBLE WAYS
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GMATT73
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Imagine a 3X2 grid as such with X in the bottom left hand 10 Nov 2005, 23:42
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I used the same approach Nakib. Any "algebraic shortcuts" to save a minute or so instead of manually counting each unique path?
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nero44
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Imagine a 3X2 grid as such with X in the bottom left hand 11 Nov 2005, 00:25
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GMATT73
I used the same approach Nakib. Any "algebraic shortcuts" to save a minute or so instead of manually counting each unique path?
Show more


Someone else (sorry cant recall who it was) suggested a very good method on this problem. since you only want to take the shortest ways, and dont want to circle around the grid, you can go along the x axis 3 times and you can go up the y axis 2 times. 5 steps in total

example: go XXXYY

now you can treat the possible ways simply as a combination problem. To put differently, in how many ways can the 3 Xs and the 2 Ys be arranged?

5!/3!*2! = 5*4/2*1 = 10 ways
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Imagine a 3X2 grid as such with X in the bottom left hand 11 Nov 2005, 00:34
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Thanks Nero,

So 5C2 to get the total number of Ys. ----->10
<or> 5C3 to get the numbers of Xs----->10

Either way we get the distinct number of possible movements. This method is a big time saver, I will include it in my flashcards. 8-)
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Imagine a 3X2 grid as such with X in the bottom left hand 11 Nov 2005, 16:27
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similar question has been discussed on this form ...
method to calculate with out counting ...

Person has to take 2 horizontal steps and 3 vertical steps
HHVVV

Find the no of Different words that can be formed by the HHVVV word characters

= (total no of characters)!/(no of each repeated character)!

= 5!/2!3!

= 10




GMATT73
Imagine a 3X2 grid as such with X in the bottom left hand corner and Y in the top right hand corner: How many possible ways can a person walk from X to Y in 5 steps (horizontal or vertical only)? The OG just reccommends visually counting all 10 ways, but surely there must be a faster way?

l----l----l
l----l----l
l----l----l
Show more



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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