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
I have 5 positions….
456
123
346
125
246
135
356
124
256
134
5-
456(123)
356(124)
346(125)
256(134)
246(135)
people who refer 6 pls list the ccombinatons, like above, showing 6.
thanks
A B C D E F – six people ordered according to ascending heights
Now it’s quite clear that ‘A’ takes first row left most position, and ‘F’ takes second row right most position.
__ __ F
A __ __
Now we are left with B, C, D and E.
The position above ‘A’ can be filled in three ways (leaving the tallest among them for the next position, as the person in next position should be taller than the person in this one.)
3 __ F
A __ __
Now we are left with three people.
The position below ‘F’ can be filled in two ways (leaving the shortest among them for the previous position, as the person in previous position should be shorter than the person in this one.)
3 __ F
A __ 2
Now we are left with two people, the taller one takes the position adjacent to F and the shorter one takes the position adjacent to A. i.e. only one possible way.
So, Total no. of ways = 3*2*1*1 = 6
@GMAT team: What is the correct answer??
OPtion A
36
B : 6 is the answer
The answer provided by Gaurav seems to be correct and also in sync with the hint from GMAT Team.
A) 5
sems to the correct answer.
Ans is E
A
Comb is
456 246 256 346 356
123 135 134 125 124
The answer is E.