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Every morning, Casey walks from her house to the bus stop. She always

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Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  04 Nov 2010, 07:05
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Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?

A. 120
B. 122
C. 124
D. 126
E. 128


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Bunuel
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  04 Nov 2010, 07:35
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krishnasty wrote:
Encountered another question and dont know how to proceed:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?


In order to travel exactly nine blocks Casey should go 5 block down and 4 block left - DDDDDLLLL.

# of permutations of 9 letters DDDDDLLLL out of which there are 5 identical D's and 4 identical L's is \(\frac{9!}{5!4!}\).

Hope it's clear.
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  18 Aug 2017, 22:53
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Agree with the solution. But, in the diagram it looks like its 8 blocks not 9 (5 on the right column and 3 on row)
Can anyone let me know what is my error here?
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  25 Sep 2013, 01:46
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krishnasty wrote:
Encountered another question and dont know how to proceed:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?


Similar questions to practice:
grockit-similar-to-og-quant-qustion-99962.html
pat-will-walk-from-intersection-a-to-intersection-b-along-a-68374.html
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  25 Sep 2013, 07:23
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The answer should be 126

9!/(4!*5!) or (9*8*7*6*5)/(4*3*2*1)
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  25 May 2014, 11:34
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Valerun wrote:
The answer should be 126

9!/(4!*5!) or (9*8*7*6*5)/(4*3*2*1)


Agree with 126 as answer

Namely 9C4 as also pointed out correctly by Quant Expert Bunuel

Answer: A

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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  07 Sep 2016, 16:29
Bunuel wrote:
krishnasty wrote:
Encountered another question and dont know how to proceed:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?


In order to travel exactly nine blocks Casey should go 5 block down and 4 block left - DDDDDLLLL.

# of permutations of 9 letters DDDDDLLLL out of which there are 5 identical D's and 4 identical L's is \(\frac{9!}{5!4!}\).

Hope it's clear.



Why it cant be 6*5 (as in 6 lines to the left and 5 lines down?

or if we are choosing blocks than 5C1 * 4C1
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  21 Sep 2016, 09:36
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sidoknowia wrote:
Bunuel wrote:
krishnasty wrote:
Encountered another question and dont know how to proceed:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?


In order to travel exactly nine blocks Casey should go 5 block down and 4 block left - DDDDDLLLL.

# of permutations of 9 letters DDDDDLLLL out of which there are 5 identical D's and 4 identical L's is \(\frac{9!}{5!4!}\).

Hope it's clear.



Why it cant be 6*5 (as in 6 lines to the left and 5 lines down?

or if we are choosing blocks than 5C1 * 4C1



sidoknowia,

Think of it like this:

There are a total of 9 turns that have to be made, 5D and 4L. In order to make find out the number of possible routes you have to think about how many different combinations of D turns you can make if there are 9 possible positions. Thinking of it like this leaves you with 9C5 = 9!/5!(9-5)! =126.

Or you cant think of it as how many combinations of L turns you cam make if there are 9 possible positions. This leaves you with 9C4 = 9!/4!(9-4)! = 126. Same answer either way.
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  28 Jan 2018, 07:25
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krishnasty wrote:
Encountered another question and dont know how to proceed:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?



to reach from start to end point one has to walk on 4 horizontal lines and 5 Vertical lines irrespective of the path chosen as only right and up movements are allowed.

Hence one of the possible route will be HHHHVVVVV

but another path could be VVHHVHHVV

i.e. all possible arrangements of these 9 letters HHHHVVVVV are different routes

the arrangements of these 9 letters can be represented by 9!/(5!*4!) which is same as 9C4 or 9C5

Alternatively we may say that out of 9 blank spaces we need to select only 4 places for H's which we can do in 9C4 ways and rest 5 places can be filled by V in just one way
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Re: Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  20 Apr 2020, 04:04
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krishnasty wrote:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?

A. 120
B. 122
C. 124
D. 126
E. 128


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Attachment:
route.jpg


total possible ways ; 9!/4!* 5! = 126
OPTION D
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Every morning, Casey walks from her house to the bus stop. She always [#permalink] New post  20 Jun 2020, 10:14
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Similar problem solved using 2 methods here



Hope it helps!
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