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A photographer will arrange 6 people of 6 different heights

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A photographer will arrange 6 people of 6 different heights [#permalink]

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New post 24 Sep 2008, 06:27
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A photographer will arrange 6 people of 6 different heights for photograph by placing
them in two rows of three so that each person in the first row is standing in front of
someone in the second row. The heights of the people within each row must increase
from left to right, and each person in the second row must be taller than the person
standing in front of him or her. How many such arrangements of the 6 people are
possible?
A. 5
B. 6
C. 9
D. 24
E. 36

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Re: Combinatory Problem - Help needed [#permalink]

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New post 24 Sep 2008, 06:28
Question is already posted.

I think answer is 5.

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Re: Combinatory Problem - Help needed [#permalink]

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New post 24 Sep 2008, 08:03
Looks like 36 is the answer if I got it right.
6 people w diff height lets assign them numbers from 1 shortest to 6 tallest

so we have 2 rows

1 2 3
4 5 6

three shortest will always stay in the back and three tallest in front row

therefore back row can be combined 1*2*3 = 6
same for front row

6x6=36
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Re: Combinatory Problem - Help needed [#permalink]

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New post 25 Sep 2008, 08:42
Solution:

There are 6 people and all have different heights.

The persons are in the back has to be taller than the person in the front.

Let's say a1, a2, a3, a4, a5, a6 are 6 persons.

The persons in ascending order based on height.

a1 < a2 < a3 < a4 < a5 < a6.

Condition: The heights of the people within each row must increase from left to right.

combinations:

1) a4 a5 a6
a1 a2 a3

2) a2 a5 a6
a1 a3 a4

3) a3 a5 a6
a1 a3 a4

4) a2 a4 a6
a1 a3 a5

5) a3 a4 a6
a1 a2 a5

So total five possibilities. Other are ignored based on above conditions.

So answer is 5.

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Re: Combinatory Problem - Help needed [#permalink]

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New post 25 Sep 2008, 10:01
Twoone wrote:
Solution:

There are 6 people and all have different heights.

The persons are in the back has to be taller than the person in the front.

Let's say a1, a2, a3, a4, a5, a6 are 6 persons.

The persons in ascending order based on height.

a1 < a2 < a3 < a4 < a5 < a6.

Condition: The heights of the people within each row must increase from left to right.

combinations:

1) a4 a5 a6
a1 a2 a3

2) a2 a5 a6
a1 a3 a4

3) a3 a5 a6
a1 a3 a4

4) a2 a4 a6
a1 a3 a5

5) a3 a4 a6
a1 a2 a5

So total five possibilities. Other are ignored based on above conditions.

So answer is 5.

Is thier any other way solve it, this solution involve lot many steps may not be fisible to attempt at GMAT.

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Re: Combinatory Problem - Help needed [#permalink]

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New post 25 Sep 2008, 10:35
vivektripathi wrote:
Is thier any other way solve it, this solution involve lot many steps may not be fisible to attempt at GMAT.


This is my solution. Just draw diagram and check each possible solution.

Case 1: Basic set up. The smallest guy on lower left and the highest guy on upper right.

4 5 6
1 2 3

You cannot move 6 down or move 1 up because this will violate the rule. Therefore, guy 2, 3, 4, and 5 will be moving around.

Case 2: Move 5 down and 3 up
3 4 6
1 2 5

Case 3: Move 5 down and 2 up
2 4 6
1 2 5

Case 4: Move 4 down and 3 up
3 5 6
1 2 4

Case 5: Move 4 down and 2 up
2 5 6
1 3 4

5 cases total. The best approach to this soltuion should be this way because there are too many conditions and the number of people are not that many.

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Re: Combinatory Problem - Help needed [#permalink]

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New post 06 May 2009, 12:45
spiridon wrote:
Looks like 36 is the answer if I got it right.
6 people w diff height lets assign them numbers from 1 shortest to 6 tallest

so we have 2 rows

1 2 3
4 5 6

three shortest will always stay in the back and three tallest in front row

therefore back row can be combined 1*2*3 = 6
same for front row

6x6=36


If you combine each row as 6!, you are not considering that the first two guys at each row must have a taller guy at his left. Its not a free combination... it has restrictions.

5 seems to be the answer for me...

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Re: Combinatory Problem - Help needed   [#permalink] 06 May 2009, 12:45
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A photographer will arrange 6 people of 6 different heights

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