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
A
should be A i.e.5
consider 1 2 3 4 5 6 to be persons in increasing order fr heights…
so the arrnagements can be
456
123
246
135
346
125
256
134
356
124
what is OA?
OA means ?
Official Answer?
Gaurav, very descriptive explanation!
see that 1 and 6 positions are constant.
once we get that fact …question seems easy.
Ans GMAT team
…6
123
…6
124
…6
125
…6
134
…6
135
This is just hint, We will give the correct answer after discussion.
D – 24, since it arrangements, 6 & 1 are fixed in the second and first row (from the camera) the remaining 4 people can occupy any of the six postions in 24 diff ways
any postion meaning – satisfying the height precedence rule
6 ways
123 (common for all) and remaining 3 in 3p2 ways =6
A – 5 ways
answer is 36 – E
There are six position.
A B C
D E F
For Position A – Number of possibilities is 3
For Position B – 2
For position C – 1
Same for D, E, F
3 * 2 * 1 * 3 * 2 * 1 = 36
TAKEGMAT – please correct me if I am wrong
Answer is A – 5 ways…
We need to remember that according to the height precedence rule, not only is left to right in increasing order of height, but the front row is also shorter than the person stadnding immediately behind.
So, even if 123 is constant, there is only ONE way to arrange the remaining people. Same applies to all other combinations. Given that the 1st and the last place can be occupied in the same way in all cases, we can work out 5 different arrangements.
answer is 5
gaurav’s explanation is perfect
A-
1,2,3,4,5,6 – people ordered by height.
Possible arrangements:
456 356 346 256 246
123 124 125 134 135
36. this is the way it can be filled.
2 3 (6)1
__ __ __
1(1) 3 3
__ __ __
6 ways.. Answer is ‘B’.
Ans is 5 using 2 rules:
1)L to R increasing order
2)back row has a taller height than the front row.
the only rows possible are as follows
456(123), 356(124), 256(134), 346(125), 246(135)
The answer is E.
A
Comb is
456 246 256 346 356
123 135 134 125 124
Ans is E
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.
B : 6 is the answer
36
OPtion A
@GMAT team: What is the correct answer??
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
5-
456(123)
356(124)
346(125)
256(134)
246(135)
people who refer 6 pls list the ccombinatons, like above, showing 6.
thanks
I have 5 positions….
456
123
346
125
246
135
356
124
256
134