Problem Solving

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

Dont have the answer sorry...

Let the heights be 1,2,3,4,5,6
C D 6
1 A B
This should be the arrangement.
Hence we are left with 4 unknown psitions A,B,C,D corresponding to 2,3,4,5 (not in the same order)

Now, for D:
D>A and D>C
Hence D should be greater than atleast 2 elements out of 2,3,4,5
Which means D can be 4 or 5

Now, for C,
C< D
So C can be 2 or 3 or 4

When D = 4, C can be 2 or 3 -> 2 ways
When D = 5, C can take 2 or 3 or 4. -> 3 ways

Hence total 5 ways.

Hope this helps!!

kvcpk wrote:Let the heights be 1,2,3,4,5,6
C D 6
1 A B
This should be the arrangement.
Hence we are left with 4 unknown psitions A,B,C,D corresponding to 2,3,4,5 (not in the same order)

Now, for D:
D>A and D>C
Hence D should be greater than atleast 2 elements out of 2,3,4,5
Which means D can be 4 or 5

Now, for C,
C< D
So C can be 2 or 3 or 4

When D = 4, C can be 2 or 3 -> 2 ways
When D = 5, C can take 2 or 3 or 4. -> 3 ways

Hence total 5 ways.

your assumption is correct ,but will explaining it is little bit confusing please explain me clearly ...........in simple method .........

likithae wrote: your assumption is correct ,but will explaining it is little bit confusing please explain me clearly ...........in simple method .........

Well, this problem is a bit difficult to explain. I found this link which has a detailed solution.
https://www.manhattangmat.com/forums/per ... -t602.html

Check this link and post back if you still have any queries.

Cheers!!

kvcpk wrote:

likithae wrote: your assumption is correct ,but will explaining it is little bit confusing please explain me clearly ...........in simple method .........

Well, this problem is a bit difficult to explain. I found this link which has a detailed solution.
https://www.manhattangmat.com/forums/per ... -t602.html

Check this link and post back if you still have any queries.

Cheers!!

thanks........... i too came across these problem... by sending a link now i can understood clearly........