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 person and 6 is the tallest person.
Fill the MOST RESTRICTED positions first and work down to the LEAST RESTRICTED positions.
Place 1 and 6:
1XX
XX
6
Place 2:
Case A:
1XX
2X6
Case B:
1
2X
XX6
Place 5, whose position will determine where 3 and 4 can go:
Case A:
1
34...1
35
2
56...2
46
Case B:
12
5...12
4...12
3
346...
356...
456
Total options = 5.
The correct answer is
A.
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