Arrangements for a photography

[yass20015]

A photograph will arrange 6 people of 6 different heights for a photography 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 with each row must increase frm left to right, and each person in the second row must be taller than the person standing in front of him/her. hOW MANY SUCH ARRANGEMENTS of the 6 people are possible ?
I got 6 but the right answer is 5. wHY ?? any answer ? Many thanks

[GMATGuruNY]

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.

The correct answer is A.

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Hi yass20015,

In Quant questions such as these, the number of possible arrangements is sometimes so limited that you can actually just list them out - in that way, you can visualize the solution and just do a bit of 'brute force' work:

Here, we're told to arrange 6 people (who all have DIFFERENT heights) into two rows of 3 so that each person in the first row is 'in front' of a taller person in the second row AND heights increase from 'left to right.' We're asked how many arrangements of people are possible.

If we label the six people as 1, 2, 3, 4, 5, 6 (with 1 the shortest, and each number being 'taller' than the one immediately preceding it), we would have the following options...

456
123

356
124

346
125

256
134

246
135

There are NO other options.

Final Answer: A

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