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

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17 Dec 2012, 07:31

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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?

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

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17 Dec 2012, 07:33

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Attachment:

Path.png [ 16.12 KiB | Viewed 8622 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.

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

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17 Dec 2012, 11:26

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.

Answer: C.

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

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

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17 Dec 2012, 11:46

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.

Answer: C.

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

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

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28 Dec 2012, 01:52

Walkabout 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

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

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

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15 Jul 2014, 03:03

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.

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

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21 Oct 2015, 15:16

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