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# How many ways are there to go from A to D, passing through

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How many ways are there to go from A to D, passing through [#permalink]

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13 Nov 2007, 07:17
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How many ways are there to go from A to D, passing through both B and C? You can only go north or east?
(See the attached)

I can't even solve this simple work.. please anybody kind for the explanation....
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13 Nov 2007, 07:41
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Is the answer 2*3*6 = 36

For reaching from A to B there are 2 ways

For reaching from B to C there are 3 ways

For reaching from C to D there are 6 ways

Therefore there are total 36 different ways to reach from A to D

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13 Nov 2007, 09:06
the sily questions,, but I really thank you guys for your kind, persistent answers....
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28 Sep 2009, 05:13
Yes. The total number of ways is 2 * 3 * 6 = 36
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25 Mar 2010, 07:16
There are actually four ways to go from B to C. so total number of ways = 2*4*6 = 48
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21 Nov 2010, 07:33
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A more structured way of looking at it:
A-B: 1 U(up) and 1 R(right), number of ways = 2 !/(1!*1!) = 2
B-C: 1 U and 2 R, number of ways= (1+2)!/(1!*2!)=3!/2! = 3
C-D: 2 U and 2 R, " = (2+2)!/(2!*2!) = 6
Total number of ways: 2*3*6 = 36

In such problems break the question into the number of U / D / L / R 's(up/down/left/right)
In almost all such problems it is given that the flow / movement is unidirectional (you cant move up in one step and down in the next).

For each such scenario determine the number of ways: (U + R)! / (U! * R!) :U, R for this example
We divide by U!(or R!) - since each U(or R) is identical.

On a similar note -
find the number of different words you can formulate from

GEORGE = 6! / (2!*2!)
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21 Nov 2010, 20:53
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pretttyune wrote:
How many ways are there to go from A to D, passing through both B and C? You can only go north or east?
(See the attached)

I can't even solve this simple work.. please anybody kind for the explanation....

First of all, the question is definitely not 'this simple'. Though once you know how to deal with such questions, it becomes quite easy.

I do agree with vicksikand. Its easy to solve it his way. Let me elaborate on the theory behind it.

When I want to go from A to B, I have to take 1 step north and 1 step east. I can do this in two ways: First north, then east or first east, then north. I can say that I have two steps N and E and I have to arrange them. I can do it in 2 ways (NE) or (EN).

When I want to go from B to C, I have to take 1 step north and 2 steps east. I can do it in three ways: First north, then east, then east (NEE) or First east, then north, then east (ENE) or first east, then east, then north (EEN).
I can say I have 3 steps NEE and I have to arrange these in different ways. It can be done in 3!/2! ways = 3 ways (We divide by 2! because we have 2 E's. For more details check permutations theory)

When I want to go from C to D, we need to take two steps north and two east. That is, we have to arrange NNEE is different ways. This can be done in 4!/2!*2! = 6 ways (NNEE) or (NENE) or (NEEN) or (EENN) or (ENEN) or (ENNE)
We divide by two 2! because N is twice and E is twice.

Total number of ways of going from A to D = 2*3*6 = 36
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29 Dec 2010, 08:29
From B to C we can go in 4 ways.
3h and 1v 4!/3!=4
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29 Dec 2010, 08:45
niraj92 wrote:
From B to C we can go in 4 ways.
3h and 1v 4!/3!=4

36 is correct: 2 ways from A to B, 3 ways from B to C (2h and 1v: 3!/2!=3) and 6 ways from C to D --> 2*3*6=36.
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Re: How many ways are there to go from A to D, passing through [#permalink]

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17 Dec 2012, 09:42
pretttyune wrote:
How many ways are there to go from A to D, passing through both B and C? You can only go north or east?
(See the attached)

I can't even solve this simple work.. please anybody kind for the explanation....

Is this a typical GMAT problem?? I've never seen problems like this. Is this a PS problem?
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Re: How many ways are there to go from A to D, passing through [#permalink]

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17 Dec 2012, 09:45
JJ2014 wrote:
pretttyune wrote:
How many ways are there to go from A to D, passing through both B and C? You can only go north or east?
(See the attached)

I can't even solve this simple work.. please anybody kind for the explanation....

Is this a typical GMAT problem?? I've never seen problems like this. Is this a PS problem?

Similar (though easier) question from OG: the-diagram-above-shows-the-various-paths-along-which-a-mous-144271.html
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Re: How many ways are there to go from A to D, passing through [#permalink]

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20 Jan 2014, 11:20
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Re: How many ways are there to go from A to D, passing through [#permalink]

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10 May 2015, 20:05
Hello from the GMAT Club BumpBot!

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Re: How many ways are there to go from A to D, passing through [#permalink]

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05 Jun 2016, 07:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many ways are there to go from A to D, passing through   [#permalink] 05 Jun 2016, 07:08
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