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# A photographer will arrange 6 people of 6 different heights

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Manager
Joined: 10 Oct 2005
Posts: 113
Location: Hollywood
A photographer will arrange 6 people of 6 different heights  [#permalink]

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11 Feb 2007, 03:41
5
00:00

Difficulty:

85% (hard)

Question Stats:

50% (00:50) correct 50% (01:02) wrong based on 107 sessions

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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 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 26

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-photographer-will-arrange-6-people-of-6-different-heights-86046.html

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Senior Manager
Joined: 04 Jan 2006
Posts: 265
Re: PS - The Photographer (How many arrangements...?)  [#permalink]

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11 Feb 2007, 08:17
1
2
TOUGH GUY wrote:
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 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 26

Interesting question:

Assuming the height of each person = 1, 2, 3, 4,5, 6 (it's irrational but the number makes it easy to compare)

From the question, we can conclude that 1 must be on the lower left and 6 must be the upper right. So 2 position are fixed.

Case 1: The most common arrangement.
4_5_6 <--- row 2
1_2_3 <--- row 1

Case 2: Bring 5 down and bring 3 up
3_4_6
1_2_5

Case 3: Bring 5 down and bring 2 up
2_4_6
1_3_5

Case 4: Bring 4 down and bring 3 up
3_5_6
1_2_4

Case 5: Bring 4 down and bring 2 up
2_5_6
1_3_4

5 cases total. The answer is A?
Director
Joined: 29 Nov 2012
Posts: 757
Re: A photographer will arrange 6 people of 6 different heights  [#permalink]

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28 Jul 2013, 22:19
1
How do you solve this one? Can someone help out. Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 52387
Re: A photographer will arrange 6 people of 6 different heights  [#permalink]

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28 Jul 2013, 22:21
fozzzy wrote:
How do you solve this one? Can someone help out. Thanks!

Check here: a-photographer-will-arrange-6-people-of-6-different-heights-86046.html
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Joined: 09 Sep 2013
Posts: 9463
Re: A photographer will arrange 6 people of 6 different heights  [#permalink]

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26 Jul 2018, 01:13
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: A photographer will arrange 6 people of 6 different heights &nbs [#permalink] 26 Jul 2018, 01:13
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