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In the array of unit squares shown in the figure above, a dotted path

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Bunuel
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In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   04 Oct 2017, 00:36
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In the array of unit squares shown in the figure above, a dotted path has been traced along the sides of the squares from A to C via B. What is the total number of different paths from A to C via B of length 6 units that can be traced along the sides of the squares?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

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D
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amanvermagmat
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In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   04 Oct 2017, 10:49
From A to B there are 2 different paths, and from B to C there are 4 different paths. Now, for each of the 2 paths from A to B, there are 4 paths from B to C. So answer should be 2*4 = 8

D answer
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   04 Oct 2017, 12:15
Bunuel wrote:

In the array of unit squares shown in the figure above, a dotted path has been traced along the sides of the squares from A to C via B. What is the total number of different paths from A to C via B of length 6 units that can be traced along the sides of the squares?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

Show Spoiler
Attachment:
2017-10-04_1122.png


Answer should be 4.
There are different ways from A towards B and there are two different ways towards C from B.
So 2*2
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Rag1217
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   05 Oct 2017, 10:57
D: 8

A to B - 2 paths and B to C - 4 different paths

A to B to C : 2*4 - 8 paths

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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   14 Nov 2017, 03:40
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I went with D.
A to B= 2 Path
B to C= 4 Path
Total Path= 2*4= 8 path.

Plz correct if I am wrong.
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 18:18
I went with D as well:
The shortest path from A to C has length 6, therefore any path that is not optimal is out.
From A to B there are only 2 optimal paths: either you go up and right or right and up.
From B to C, you need to walk 3 ups and one right, in any order (UUUR, UURU, URUUU, RUUU).
(2 ways from A to B)*(4 ways from B to C) = 8 paths
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 20:19
Bunuel wrote:

In the array of unit squares shown in the figure above, a dotted path has been traced along the sides of the squares from A to C via B. What is the total number of different paths from A to C via B of length 6 units that can be traced along the sides of the squares?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

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Attachment:
2017-10-04_1122.png


Hi Bunuel, genxer123, chetan2u,

Can you please provide the OE for this question? I am getting 8 as the answer but the OA is 4 :cry:
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Henry S. Hudson Jr.
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 20:27
The sequence can be thought of as Up, Right, Up, Up, Up, Right

We have to consider permutations now.

We have to either begin going Up right

or Right up

let's consider up right and then multiply by 2 to account for right up.

Up, Right, Up , Up , Up Right

We are now only concerned with the highlighted part. U, U, U, R can occur in 4 different ways (the R can be in any of one spaces). We have to now multiply by 2 to account for the right, up start. 4(2)=8
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chetan2u
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 20:40
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rahul16singh28 wrote:
Bunuel wrote:

In the array of unit squares shown in the figure above, a dotted path has been traced along the sides of the squares from A to C via B. What is the total number of different paths from A to C via B of length 6 units that can be traced along the sides of the squares?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

Show Spoiler
Attachment:
2017-10-04_1122.png


Hi Bunuel, genxer123, chetan2u,

Can you please provide the OE for this question? I am getting 8 as the answer but the OA is 4 :cry:


Hi..

different paths from A to C via B with length 6 units basically means the shortest path..
so from B to C , there are 3 vertical steps and 1 horizontal step, and it can have 4 ways...
A to B is 1 horizontal and 1 vertical and it can have 2 ways

total 2*4 = 8

so the OA should be 8 itself..
Bunuel, must be some typo in OA
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Bunuel
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 20:44
Expert Reply
Bunuel wrote:

In the array of unit squares shown in the figure above, a dotted path has been traced along the sides of the squares from A to C via B. What is the total number of different paths from A to C via B of length 6 units that can be traced along the sides of the squares?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

Show Spoiler
Attachment:
2017-10-04_1122.png


The OA is D. Edited. Thank you.
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 22:22
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amanvermagmat

Quote:
From A to C there are 2 different paths, and from C to B there are 4 different paths. Now, for each of the 2 paths from A to C, there are 4 paths from C to B. So answer should be 2*4 = 8


Did you mean A to B has 2 different paths?
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink] New post   20 Dec 2017, 23:34
adkikani wrote:
amanvermagmat

Quote:
From A to C there are 2 different paths, and from C to B there are 4 different paths. Now, for each of the 2 paths from A to C, there are 4 paths from C to B. So answer should be 2*4 = 8


Did you mean A to B has 2 different paths?


Oh yes, that was a typo. I have edited it now, Thank you.
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Re: In the array of unit squares shown in the figure above, a dotted path [#permalink]
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