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Permutation and combination question

  • Thread starter gaobo9109
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Homework Statement


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)


Homework Equations





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
 

Answers and Replies

  • #2
vela
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Homework Statement


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)


Homework Equations





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
6x24=144, not 360.
Form two groups of 2: 4C2/2 x 6P2 = 90
I'm too tired to figure out what you're doing, but I got 360 for this case.
Form two groups of 1 and 3: 4 x 6P2 = 120
And 720 for this case.
Form three groups of 1,1 and 2: 4 x 3 x 6P3 = 1440
All separated: 6P4 = 360
We agree on these cases.
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
 

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