## GMAT Prep Exam Pack 1 - Arranging/FPC Question

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### GMAT Prep Exam Pack 1 - Arranging/FPC Question

by s777 » Tue Dec 10, 2013 7:48 am
A photographer will arrange 6 people of 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 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

Can someone help me solve this ?

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by GMATGuruNY » Tue Dec 10, 2013 8:09 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, where 1 is the shortest and 6 is the tallest.
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.