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# The diagram above shows the various paths along which a mous

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The diagram above shows the various paths along which a mous [#permalink]  17 Dec 2012, 06:31
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83% (01:36) correct 17% (00:54) wrong based on 416 sessions
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The diagram above 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 pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17
[Reveal] Spoiler: OA
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Re: The diagram above shows the various paths along which a mous [#permalink]  17 Dec 2012, 06:33
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Path.png [ 16.12 KiB | Viewed 6114 times ]
The diagram above 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 pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

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Re: The diagram above shows the various paths along which a mous [#permalink]  11 Sep 2013, 00:43
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Re: The diagram above shows the various paths along which a mous [#permalink]  17 Dec 2012, 06:56
Expert's post
Also counting is fast

12 or 11 paths. 12 is the only among the options.

So C
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Re: The diagram above shows the various paths along which a mous [#permalink]  17 Dec 2012, 10:26
Bunuel wrote:
Attachment:
Path.png
The diagram above 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 pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Dear Bunnel,
Could you please clarify it more...How the forks are working?
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Re: The diagram above shows the various paths along which a mous [#permalink]  17 Dec 2012, 10:46
Expert's post
Drik wrote:
Bunuel wrote:
Attachment:
Path.png
The diagram above 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 pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Dear Bunnel,
Could you please clarify it more...How the forks are working?

is pretty simple: one the first fork you have 2 choices - right and left; idem for the second one; 3 for the third one: right, left and central to the goal. 2*2*3=12

That's it
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Re: The diagram above shows the various paths along which a mous [#permalink]  28 Dec 2012, 00:52
Attachment:
Path.png
The diagram above 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 pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

Technique here is to multiply the number of choices in every point of decision:
$$2*2*3 = 12$$

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Re: The diagram above shows the various paths along which a mous [#permalink]  10 Sep 2013, 22:24
Hi Brunel - Would you help us with more such questions?
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Re: The diagram above shows the various paths along which a mous [#permalink]  15 Jul 2014, 01:49
Why is it multiplied here ? Why can't we add all options ?

Posted from my mobile device
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Re: The diagram above shows the various paths along which a mous [#permalink]  15 Jul 2014, 02:03
Expert's post
kshitij89 wrote:
Why is it multiplied here ? Why can't we add all options ?

Posted from my mobile device

Because of 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.

For example, if you have two pairs of shoes, A and B, and two shirts, X and Y, then there will be 2*2 = 4 shoes-shirt combinations:
AX;
AY;
BX;
BY.

Hope it's clear.
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Re: The diagram above shows the various paths along which a mous   [#permalink] 15 Jul 2014, 02:03
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