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Permutations Question - HELP

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by soni_pallavi » Mon Oct 29, 2012 1:02 am
Hi

Could someone explain this question.

A photographer will arrange 6 people with 6 different heights for a 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 people of 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.How many arrangement of the 6 people are possible?

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by Shailesh02 » Mon Oct 29, 2012 1:35 am
Arrange 6 people in two rows in increasing height in each row. Also every person standing behind should be taller than person standing in front of him.
Answer should be 36.
soni_pallavi wrote:Hi

Could someone explain this question.

A photographer will arrange 6 people with 6 different heights for a 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 people of 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.How many arrangement of the 6 people are possible?

Thanks
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by soni_pallavi » Mon Oct 29, 2012 2:08 am
The answer in the book is 5.Thats what got me confused.
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by GMATGuruNY » Mon Oct 29, 2012 4:18 am
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 some one in second row. The heights of the people with in each row should be increasing from left 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
Let the 6 people be represented by the numbers 1-6, inclusive.
Fill the MOST RESTRICTED positions first and work down to the LEAST RESTRICTED positions.

Place 1 and 6:
XX6
1XX

Place 2:
Case A:
2X6
1XX

Case B:
XX6
12X

Place 5, whose position will determine where 3 and 4 can go:
Case A:
256...246
134...135

Case B:
346...356...456
125...124...123

Total options = 5.
The correct answer is A.
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