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Permutation and combination question

  1. Mar 25, 2010 #1
    1. The problem statement, all variables and given/known data
    A photographer is positioning 5 men and 4 women for a photo shoot. The men are positioned in the order from shortest on the left to tallest on the right. Find the number of ways the photographer can position them in a row. (All men are of different heights and are not necessarily standing together in a group)


    2. Relevant equations



    3. The attempt at a solution
    Since the position of men are fixed, i will just consider the possible permutation of women.

    Four women can either stand together as one group, or split into two, three or four groups.

    Below are combination forl 5 possible cases
    Grouped together: 6 x 4! = 360
    Form two groups of 2: 4C2/2 x 6P2 = 90
    Form two groups of 1 and 3: 4 x 6P2 = 120
    Form three groups of 1,1 and 2: 4 x 3 x 6P3 = 1440
    All separated: 6P4 = 360

    Then I added up all the possible combinations. The answer I obtained is 2154. However, the answer provided is 3024. Can anyone tell me which case I fail to consider? Or is there anything wrong with my working? Thanks
     
  2. jcsd
  3. Mar 25, 2010 #2

    vela

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    6x24=144, not 360.
    I'm too tired to figure out what you're doing, but I got 360 for this case.
    And 720 for this case.
    We agree on these cases.
     
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