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The diagram below shows the various paths along which a [#permalink]

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25 Apr 2012, 07:54

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The diagram below shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pallet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracting any point along a path?

Re: The diagram below shows the various paths along which a [#permalink]

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25 Apr 2012, 08:15

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emil3m wrote:

The diagram below shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pallet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracting any point along a path?

A. 6 B. 7 C. 12 D. 14 E. 17

I know my approach is wrong. Can you please help me understand why the permutation formula does not work for this problem? ( We are counting without replacement and the order matters, so I tried n!/(n-3)! where n=7

Thank you, all!

It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Re: The diagram below shows the various paths along which a [#permalink]

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25 Apr 2012, 08:25

Bunuel wrote:

It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.

7 paths to chose from and you must pick 3 to get to the destination..

I haven't seen a permutation problem yet in the OG, so maybe the difference in identifying when to use it will show when I see one.

Re: The diagram below shows the various paths along which a [#permalink]

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25 Apr 2012, 08:31

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emil3m wrote:

Bunuel wrote:

It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.

7 paths to chose from and you must pick 3 to get to the destination..

I haven't seen a permutation problem yet in the OG, so maybe the difference in identifying when to use it will show when I see one.

As you can see from the solution there are 12 different paths not 7. There are 2+2+3=7 different line segments separated by 3 forks.

Re: The diagram below shows the various paths along which a [#permalink]

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30 Aug 2013, 09:03

Bunuel wrote:

emil3m wrote:

Bunuel wrote:

It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.

Buneul, Could you please explain why the answer is 12 and not 7. Since there are 7 separate forks, how could there be twelve separate ways the mouse could travel? Why are you multiplying the numbers instead of adding?

Re: The diagram below shows the various paths along which a [#permalink]

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31 Aug 2013, 05:57

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anujkhatiwada wrote:

Bunuel wrote:

emil3m wrote:

It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.

Buneul, Could you please explain why the answer is 12 and not 7. Since there are 7 separate forks, how could there be twelve separate ways the mouse could travel? Why are you multiplying the numbers instead of adding?

Thanks!

There are 3 forsk not 7:

As for multiplication: it's called Principle of Multiplication. If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in m*n ways.

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