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

Question

https://gmatclub.com/forum/download/file.php?id=81420 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 route.jpg GMAT-Club-Forum-9w6idxcw.png

Bunuel · Accepted Answer

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.

Madhavi1990 · Answer

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?

Bunuel · Answer

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

Valerun · Answer

The answer should be 126

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

jlgdr · Answer

Agree with 126 as answer Namely 9C4 as also pointed out correctly by Quant Expert Bunuel Answer: A Cheers J

sidoknowia · Answer

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

austinlm · Answer

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.

GMATinsight · Answer

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

BrushMyQuant · Answer

In the diagram by block they mean the lines she needs to traverse. So 4 such lines/blocks to the right and 5 such lines/blocks to the top as shown below. Blocks.jpg Similar problem solved using 2 methods here https://www.youtube.com/watch?v=YkdWxXZ05P4 Hope it helps!

ShreyaG7 · Answer

I have the same doubt!

Bunuel  can you please help with this? Why are we taking 9! and not 8!?

Bunuel · Answer

Here is an image that might help. Count the number of the line segments: https://gmatclub.com/forum/download/file.php?id=82532 GMAT-Club-Forum-rrozjtpi.png

ShreyaG7 · Answer

Oh yes, that makes it very clear. Thank you Bunuel

GMAT-Club-Forum-9camqlue.png

pussycat123 · Answer

There is another right she takes hence 9

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

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