MGMAT Guide 4 Word Translations p185 Chapter 12 4th edition

[woodenfootspa]

Hi!

I am having some problems with this example from the book

" Alicia Lives in a town whose streets are on a grid system with all the streets running E-W or N-S without breaks....."

(Forgive me for not typing out the whoel question as it was fairly lengthy)

Why is the total number of possibilities 6!/ (3!*3!)?
Shouldnt we be using the slot method (with 6 slots) as she can only choose between South and East at every turn? So...

2*2*2*2*2*2?

She doesnt have 6 choices at the 1st choice. Nor 5 at the 2nd....

[tim]

She can't choose between E and S at every turn; if so, that would mean a path of EEEEEE or SSSSSS would work. The path she takes must include 3 Es and 3 Ss. So basically we have 6 steps, 3 of which must be E and 3 of which must be S. That's why you have to do 6!/(3!3!)..

[jp.jprasanna]

Hi Tim - Im trying to relate to this problem under discussion with -http://www.pagalguy.com/forums/gmat-and-gre-prep/manhattan-gmat-700%2B-problem-june-26-2006-t-16589/p-529955 , which also I believe a MGMT CAT problem

Below is the complete question with the bold part changed..

Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-sooth without breaks. Her school, located on a corner, lies three blocks south and three blocks east of his home, also located on a corner. If Alicia is equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability that of the first 3 paths she chooses, 2 will south ?

Probability = Favourable outcome / Total outcome

Total outcome = 20

Favorable outcome = atleast 2 south or all 3 south

All 3 south (nos of ways to select 3 south for the 3 paths) :::

3!/3! = 1

Atleast 2 south :::

1 ->For the 1st 3 path she needs to go 2 south so 3!/2! 1! = 3
2 -> For the rest 3 path again south step can be for any path so
South North North , NSN , NNS essentially 3!/2! 1! = 3

1 Multiplied with 2 => 3*3 = 9

Therefore

Favorable outcome = atleast 2 south or all 3 south
= 9 +1
So the probability for Alicia to take at least 2 steps south of the 1st 3 paths will be 9+1 /20 = 10/20

Is this sol / reasoning correct? I sincerely appreciate your help.

Cheers

[tim]

no. the problem here appears to be that you have misinterpreted "first three paths" (admittedly it is confusing wording, and FWIW this is NOT one of ours as near as i can tell). this problem is actually much easier than typical block-walking problems, because no matter what choices Alicia makes she can choose south or east at each of the first three opportunities. after this of course, further choices may be constrained by the choices Alicia has made to that point. as it is, though, this is no different from asking what the probability is of getting heads twice when flipping a coin three times..