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

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Every morning, Casey walks from her house to the bus stop [#permalink]

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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?
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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 [#permalink]

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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Every morning, Casey walks from her house to the bus stop [#permalink]

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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 [#permalink]

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New post 25 May 2014, 11:34
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

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Re: Every morning, Casey walks from her house to the bus stop [#permalink]

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New post 07 Sep 2016, 16:29
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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 [#permalink]

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New post 21 Sep 2016, 09:36
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 [#permalink]

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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   [#permalink] 18 Aug 2017, 22:53
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