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Alicia lives in a town whose streets are on a grid system [#permalink]
 01 Feb 2012, 11:05
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Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?
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Re: Alicia lives in a town whose streets are on a grid system [#permalink]
01 Feb 2012, 11:27
sdas wrote: Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks? To get to the school Alicia should walk 3 times south and 3 times east: SSSEEE. Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical); Now, we wan to count all the routs which start with {SS}. So, {SS} is fixed and then there can be any combination of the rest 4 letters SEEE. So, all possible routs which start with {SS} equal to # of permutation of SEEE, which is 4!/3!=4 (# of permutations of 4 letters out of which 3 E's). P=4/20=1/5.
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Re: Alicia lives in a town whose streets are on a grid system [#permalink]
01 Feb 2012, 11:46
Thanks Bunuel: the only part I was making mistake was (SS) to be considered 1 and then SEEE as 4. I was considering it as (SS) = 1 + SEEE (4) total 5. Thats why I was going wrong.
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Re: Alicia lives in a town whose streets are on a grid system [#permalink]
15 Jan 2013, 05:20
Hello,
I have a question to Bunuel. the formula you are using is Combination's formula as it is 6!/(6-3)!*3!, and since Alice has to choose 3 Ss and 3Es, where order does not matter, it has to be Combination. but you are saying that "Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical)"[u][/u]. can you please explain whether it should be a combination or permutation formula?
I am having hard time understanding this problem. Manhattan guide explains it with anagram grid, but I am not grasping that model. I tried to solve it using Slot Method, but could not do it. I can't really get it with combination/permutation formulas either. can you please explain it in an easier way with more details?
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Re: Alicia lives in a town whose streets are on a grid system
[#permalink]
15 Jan 2013, 05:20
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