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# A photographer will arrange 6 people of 6 different heights

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Manager
Joined: 06 Nov 2008
Posts: 53
A photographer will arrange 6 people of 6 different heights [#permalink]

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11 Dec 2008, 17:58
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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SVP
Joined: 29 Aug 2007
Posts: 2452

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11 Dec 2008, 22:29
haichao 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 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

suppose: six models are 1, 2, 3, 4, 5, and 6 and they are in the order that 1<2<3<4<5<6. so

a.
6 5 4
3 2 1

b.
6 5 3
4 2 1

c.
6 5 2
4 3 1

d.
6 4 3
5 2 1

e.
6 4 2
5 3 1
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Intern
Joined: 22 Dec 2007
Posts: 5

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11 Dec 2008, 23:28
This is very tough prb. please I also need a esiest solution of this. thanks
Manager
Joined: 27 May 2008
Posts: 197

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12 Dec 2008, 00:38
can it be E

suppose: six models are 1, 2, 3, 4, 5, and 6 and they are in the order that 1<2<3<4<5<6. so

since it is the arrangement, and the heights of the people within each row must increase from left to right,

1st row can be arranged in 3*2 ways
and for each person in first row 3 person can be arranged in the second row, so 6*6 = 36
Manager
Joined: 27 May 2008
Posts: 197

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12 Dec 2008, 00:43
Agreed with A

just left out the individual order of the row.
Manager
Joined: 14 Oct 2008
Posts: 160

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12 Dec 2008, 05:28
I dont think there is any shortcut for this problem. You have to check it manually to see how many possibilities are there. The QA indeed looks to be 5 ways which is A.
Intern
Joined: 31 Dec 2008
Posts: 11

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13 Jan 2009, 19:28
If you draw 2 parallel rows and write corresponding numbers 1,2,3 and 4,5,6 from left to right, we can figure out that postion 1, 5 and 6 has to filled by only fixed people i.e of height 1,5, 6 corrospondingly. For remaining 3 palces we can arrange 2,4,5 in 3*2*1 ways = 6

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This is not a quality discussion. It has been retired.

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Re: rows   [#permalink] 13 Jan 2009, 19:28
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# A photographer will arrange 6 people of 6 different heights

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