A photographer will arrange 6 people

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

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31 Comments Post a Comment
  1. gaurav says:

    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?

  2. James says:

    OA means ?

  3. solidcolor says:

    Official Answer?

    Gaurav, very descriptive explanation!

  4. krishna says:

    see that 1 and 6 positions are constant.
    once we get that fact …question seems easy.

  5. Ardhendu says:

    Ans GMAT team

  6. …6
    123

    …6
    124

    …6
    125

    …6
    134

    …6
    135

  7. This is just hint, We will give the correct answer after discussion.

  8. sudhish says:

    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

  9. sudhish says:

    any postion meaning – satisfying the height precedence rule

  10. Did says:

    6 ways

    123 (common for all) and remaining 3 in 3p2 ways =6

  11. AP says:

    A – 5 ways

  12. kishgem says:

    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

  13. Vibz says:

    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.

  14. john says:

    answer is 5
    gaurav’s explanation is perfect

  15. Looser says:

    1,2,3,4,5,6 – people ordered by height.
    Possible arrangements:
    456 356 346 256 246
    123 124 125 134 135

  16. duke says:

    36. this is the way it can be filled.

    2 3 (6)1
    __ __ __

    1(1) 3 3
    __ __ __

  17. Binita says:

    6 ways.. Answer is ‘B’.

  18. Eman says:

    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)

  19. Amitav says:

    The answer is E.

  20. Sharath says:

    A
    Comb is
    456 246 256 346 356
    123 135 134 125 124

  21. daniella sankar says:

    Ans is E

  22. Praveen says:

    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.

  23. krishna74 says:

    B : 6 is the answer

  24. Dharm says:

    OPtion A

  25. Shal says:

    @GMAT team: What is the correct answer??

  26. Pankaj Dahiya says:

    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

  27. vic says:

    5-
    456(123)
    356(124)
    346(125)
    256(134)
    246(135)

    people who refer 6 pls list the ccombinatons, like above, showing 6.

    thanks

  28. Kofi DL says:

    I have 5 positions….

    456
    123

    346
    125

    246
    135

    356
    124

    256
    134

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