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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GMATinsight
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Assuming the height of each person = 1, 2, 3, 4,5, 6abhasjha 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
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.
Answer: Option A
Last edited by GMATinsight on Mon Jul 28, 2014 4:36 am, edited 1 time in total.
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Let the 6 people be represented by the numbers 1-6, inclusive, where 1 is the shortest person and 6 is the tallest person.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
Fill the MOST RESTRICTED positions first and work down to the LEAST RESTRICTED positions.
Place 1 and 6:
1XX
XX6
Place 2:
Case A:
1XX
2X6
Case B:
12X
XX6
Place 5, whose position will determine where 3 and 4 can go:
Case A:
134...135
256...246
Case B:
125...124...123
346...356...456
Total options = 5.
The correct answer is A.
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