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# 4 couples wish to stand in a row for a group of photo. How

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VP
Joined: 22 Nov 2007
Posts: 1079

Kudos [?]: 678 [0], given: 0

4 couples wish to stand in a row for a group of photo. How [#permalink]

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16 Dec 2007, 02:11
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

4 couples wish to stand in a row for a group of photo. How many arrangements of the 8 people are possibile if each person must stand next to his or her partner?

A. 324
B. 352
C. 384
D. 426
E. 512

Kudos [?]: 678 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4576 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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16 Dec 2007, 02:18
C

N=4!*(2C1)^4=24*16=384

Kudos [?]: 4576 [0], given: 360

VP
Joined: 22 Nov 2007
Posts: 1079

Kudos [?]: 678 [0], given: 0

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16 Dec 2007, 03:10
yes...good...see my next one

Kudos [?]: 678 [0], given: 0

Intern
Joined: 13 Jun 2007
Posts: 48

Kudos [?]: 9 [0], given: 0

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16 Dec 2007, 06:56
"Walker" i agree with the answer but what is the logic you used?
For example i came to the same answer by

4P4 give all the SETS of 4 couple arrangements
2P2 gives the arrangement within a couple
2P2^4 gives the total arrangement within one set

4P4 * 2P2^4

Why did you use 2C1?

Kudos [?]: 9 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4576 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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16 Dec 2007, 07:33
alexperi wrote:
Why did you use 2C1?

2C1=2 means two different cases for first position in a couple.

I think your way is better one in general. Because nPn is more appropriate in the case of subsets with more than two members.

nPn=nC1*(n-1)C1*...*1C1 - is general relation between our ways

Kudos [?]: 4576 [0], given: 360

16 Dec 2007, 07:33
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