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Seating Arrangement

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by edvhou812 » Sun Jun 19, 2011 5:13 pm
Because it is asking for arrangements. nPr is used when order matters, nCr is used when order does not matter.
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by MBA.Aspirant » Sun Jun 19, 2011 5:25 pm
How does order matter here?

they could sit ABCDEF BADCEF ..etc
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by edvhou812 » Sun Jun 19, 2011 5:32 pm
MBA.Aspirant wrote:How does order matter here?

they could sit ABCDEF BADCEF ..etc
The question says, "what's the number of possible arrangements", so I'd say it is a permutation. I admit that probability is not my strong point though, so perhaps someone who is stronger in the subject can weigh in.
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by stuffstuff » Sun Jun 19, 2011 5:51 pm
the relative order in which people are seated matters, but the start and end point do not.

because for each permutation there will be exactly 5 duplicates (or 6 total), i think you just need to do 6! and divide it by 6 to get 120.
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by ma127 » Sun Jun 19, 2011 7:17 pm
in this form of question, the only correct answer is
- if the start point matters it is 6!, otherwise 6!/6
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by Jim@Knewton » Sun Jun 19, 2011 9:17 pm
Q: 6 people to be arranged around a circular table, what's the number of possible arrangements?
Why is this a 'permutation'?

This would be a combination if order of arrangement did not matter (Example: Number of ways to select 4 out of 6).

Here the order of arrangement matters and hence it is a permutation.
6 people around a circular table
Permutation of 6 people = 6P6 = 6*5*4*3*2*1 = 720
***The arrangement differs because abcdef is different from acbdef, and so on...

BUT they are seated around a circular table => abcdef = bcdefa = cdefab = defabc = efabcd = fabcde .........because there is no "starting point" for a circular arrangement!
=> For every 6 possible permutations only one is unique because of the circular positioning
=> Number of different possible seating arrangements = 720/6 = 120

You can generalize this principle for all simple circular arrangements of N objects to (N-1)P(N-1) permutations.
=> For an arrangement of 7 persons around a circular table, we can have 6P6 = 720 unique possibilities.

I hope this explanation helps!
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by dshan80 » Tue Jun 21, 2011 9:56 am
Knewtonian wrote:Q: 6 people to be arranged around a circular table, what's the number of possible arrangements?
Why is this a 'permutation'?

This would be a combination if order of arrangement did not matter (Example: Number of ways to select 4 out of 6).

Here the order of arrangement matters and hence it is a permutation.
6 people around a circular table
Permutation of 6 people = 6P6 = 6*5*4*3*2*1 = 720
***The arrangement differs because abcdef is different from acbdef, and so on...

BUT they are seated around a circular table => abcdef = bcdefa = cdefab = defabc = efabcd = fabcde .........because there is no "starting point" for a circular arrangement!
=> For every 6 possible permutations only one is unique because of the circular positioning
=> Number of different possible seating arrangements = 720/6 = 120

You can generalize this principle for all simple circular arrangements of N objects to (N-1)P(N-1) permutations.
=> For an arrangement of 7 persons around a circular table, we can have 6P6 = 720 unique possibilities.

I hope this explanation helps!
this blew my mind, as I kept getting 720 :) . is this one of the trickier quant problems one would see on the GMAT? im just starting to study the math side now..
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by GMATGuruNY » Tue Jun 21, 2011 10:07 am
MBA.Aspirant wrote:6 people to be arranged around a circular table, what's the number of possible arrangements?
Let's say that the 6 people are ABCDEF.

If we were to count the ways to arrange ABCDEF in a line, the following would qualify as different arrangements:

ABCDEF
BCDEFA
CDEFAB
DEFABC
EFABCD
FABCDE

But when put around a table, all of the above would qualify as only one arrangement, because the clockwise order would always be the same: A-B-C-D-E-F. In all of the above, B would be directly to the right of A; C would be directly to the right of B; D would be directly to the right of C; E would be directly to the right of D; and F would be directly to the right of E.

Thus, the number of ways to arrange N people around a circular table is smaller than the number of ways to arrange the N people in a line:

Number of ways to arrange N people around a circular table = (N-1)!.

So given 6 people, there are (6-1) = 5! = 120 ways to arrange them around a circular table.
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by navami » Wed Jun 22, 2011 4:47 am
120 is the correct answer.
As this is circular arrangement ans is n!/n
This time no looking back!!!
Navami
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