A cameraman wants to arrange six students of six different heights for

Question

A cameraman wants to arrange six students of six different heights for a picture by placing them in two rows of three such that each student in the first row stands in front of a student in the second row. The heights of the students within each row must increase from left to right, and each student in the second row must be taller than the student standing in front of him. How many such arrangements of the six students are possible?

(A) 4
(B) 5
(C) 6
(D) 12
(E) 24

Show Answer

Official Answer

B

(A) 4
(B) 5
(C) 6
(D) 12
(E) 24

AvidDreamer09 · Answer

IF 1 is the shortest and 6 is the tallest. 
1 has to be on the first row left and 2 has to be on the second row right so their position is fixed
_ _ 6
1 _ _

To make this simpler arrange the ways in which the first row can be arranged apart from 1

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54 
45(4 will be ahead of 3 or 2)

Possible combinations for the first row 23, 24, 25,34,35 so answer 5

Anurag06 · Answer

Hi

Can you please explain this step ?

Arrangement that will not be valid according to left to right restriction 32, 42, 43, 52, 53, 54 
45(4 will be ahead of 3 or 2)

I couldn't quite grasp it considering the above 2 restrictions on either ends.

Bunuel · Answer

We have two conditions to meet:
1. The heights of the students within each row must increase from left to right
2. Each student in the second row must be taller than the student standing in front of him.

For example, 3 - 2, won't be valid according to 1 and 4 - 5, in the first row won't be valid according to 2 (there are no two students taller than they are to stand behind them in the second row)

Anurag06 · Answer

Thank you Bunuel.

I had not considering ranking system from 1 to 6 which will be low to high respectively. Second mistake was regarding 32 as it would violate left to right order in row of shorter people.

judsonvpires · Answer

Could someone post an alternative explanation? Perhaps with or referencing the combinations formula? I'm not sure how to translate the restricitons on that formula. Thank you in advance.

Anurag06 · Answer

_ _ 6 (taller height)
1 _ _ (shorter height)
 2 3
 2 4
 2 5
 3 4
 3 5

Except this five if you inter change any values then considering from 1 (extreme shortest) to 6 (extreme tallest) you would violate condition 1 and since it is mentioned the above row here would be always *higher* and below row as *lower* in terms of height comparison.
 i.e. _ _ 6 (shown above) if you use another value, then it would violate second condition.

Try plugging different values and check yourself. Hope this helps!

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A cameraman wants to arrange six students of six different heights for

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