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# A photographer will arrange 6 people of 6 different heights

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Intern
Joined: 10 Oct 2008
Posts: 14
A photographer will arrange 6 people of 6 different heights [#permalink]

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17 Oct 2008, 08:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Intern
Joined: 13 Oct 2008
Posts: 8

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19 Oct 2008, 18:10
hmmm. I'd say A

SVP
Joined: 17 Jun 2008
Posts: 1529

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20 Oct 2008, 04:39
It should be C.

If we denote the persons in the increasing order of height with numbers then, these would be
1,2,3,4,5,6

Now, in the first row, first place can be occupied only by one person - 1.
Second place can be occupied by 2,3,4 - total 3.
Third place can be occupied by 3,4,5 - total 3.

Hence, total of 1*3*3 = 9 possibilities.
Director
Joined: 14 Aug 2007
Posts: 726

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20 Oct 2008, 05:25
scthakur wrote:
It should be C.

If we denote the persons in the increasing order of height with numbers then, these would be
1,2,3,4,5,6

Now, in the first row, first place can be occupied only by one person - 1.
Second place can be occupied by 2,3,4 - total 3.
Third place can be occupied by 3,4,5 - total 3.

Hence, total of 1*3*3 = 9 possibilities.

can you explain the parts I have marked red above.

IMHO, Second place can NOT be occupied by "4"
Manager
Joined: 09 Oct 2008
Posts: 93

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20 Oct 2008, 07:45
1,2,3
4,5,6
Total combination:6 ..only last row changes are possible. 3! = 6

1,3,4
2,5,6 or 2,6,5
Total combination:2..2's position will be fixed in second row.

1,3,5
2,4,6
Total combination:1..all position in second row will remain fixed

Total: 6+2+1 = 9

Thanks
Vishal Shah
SVP
Joined: 17 Jun 2008
Posts: 1529

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20 Oct 2008, 10:07
alpha_plus_gamma wrote:
scthakur wrote:
It should be C.

If we denote the persons in the increasing order of height with numbers then, these would be
1,2,3,4,5,6

Now, in the first row, first place can be occupied only by one person - 1.
Second place can be occupied by 2,3,4 - total 3.
Third place can be occupied by 3,4,5 - total 3.

Hence, total of 1*3*3 = 9 possibilities.

can you explain the parts I have marked red above.

IMHO, Second place can NOT be occupied by "4"

You are right. I made a mistake in a hurry. There are only 5 possible arrangements.

Possible arrangements:
1 2 3
4 5 6

1 2 4
3 5 6

1 2 5
3 4 6

1 3 4
2 5 6

1 3 5
2 4 6
VP
Joined: 30 Jun 2008
Posts: 1026

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20 Oct 2008, 10:12
scthakur wrote:

There are only 5 possible arrangements.

Possible arrangements:
1 2 3
4 5 6

1 2 4
3 5 6

1 2 5
3 4 6

1 3 4
2 5 6

1 3 5
2 4 6

How do we arrive at this apart from enumeration?
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

VP
Joined: 17 Jun 2008
Posts: 1373

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20 Oct 2008, 13:48
chenhong1224 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

I got 5

say the numbers are

im just listing the options !!!
1)
653
421

2)652
431

3)
643
521

4)
653
421

5)
642
531
IMO E
_________________

cheers
Its Now Or Never

SVP
Joined: 17 Jun 2008
Posts: 1529

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20 Oct 2008, 22:45
amitdgr wrote:
How do we arrive at this apart from enumeration?

Since the combination is small, I would use enumeration only as this eliminates chance of error.
Manager
Joined: 21 May 2008
Posts: 85

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21 Oct 2008, 00:24
Agree with scthakur. Since 1 and 6 are fixed, there are only 4 people left to arrange according to the stipulated rule.
Re: photographer   [#permalink] 21 Oct 2008, 00:24
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# A photographer will arrange 6 people of 6 different heights

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