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# PS-Arrangement

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Senior Manager
Joined: 05 Jun 2008
Posts: 294

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02 Dec 2008, 08:29
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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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Joined: 30 Apr 2008
Posts: 1855
Location: Oklahoma City
Schools: Hard Knocks

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02 Dec 2008, 09:43
6 or 9....my guess is 9.

Sorry I don't have time to go through my thoughts on this except that the shortest and tallest are stuck and cannot move.

vivektripathi 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

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SVP
Joined: 17 Jun 2008
Posts: 1507

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02 Dec 2008, 12:53
Let us assume that height of six people are 1,2,3,4,5,6.

Now arrangements:

1,2,3
4,5,6

1,3,4
2,5,6

1,3,5
2,4,6

1,2,4
3,5,6

1,2,5
3,4,6
Senior Manager
Joined: 05 Jun 2008
Posts: 294

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03 Dec 2008, 05:47
scthakur wrote:
Let us assume that height of six people are 1,2,3,4,5,6.

Now arrangements:

1,2,3
4,5,6

1,3,4
2,5,6

1,3,5
2,4,6

1,2,4
3,5,6

1,2,5
3,4,6

Thakur, is there any other way to do it
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Joined: 17 Jun 2008
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04 Dec 2008, 03:44
Actually, since the number was small, I enumerated the possibilities.
Manager
Joined: 08 Aug 2008
Posts: 229

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04 Dec 2008, 12:25
i would also guess 5.
look at this way:-
1 and 6 are static. we are left with 2,3,4,5.
now the 2nd pos on 1st row and 1st pos on sec row can only be filled by 2 or 3.
using 2, i can fill in 3 different arrangements with 3,4,5 at the end of 1st row-3 ways
using 3, i can have only 2 arrangements with 4 or 5 at the end of 1st row-2 ways

since these 2 arrangements also account for simultaneous positions vertically and horizontally,
Re: PS-Arrangement   [#permalink] 04 Dec 2008, 12:25
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