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If we have 8 people in a meeting, in how many ways they can sit around

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If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post Updated on: 26 Mar 2015, 03:33
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If we have 8 people in a meeting, in how many ways they can sit around a table?

A) 10*9!
B) 9*8!
C) 8*7!
D) 7*6!
E) 6*5!

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Originally posted by saeedt on 14 Apr 2011, 04:25.
Last edited by Bunuel on 26 Mar 2015, 03:33, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 14 Apr 2011, 04:33
1
saeedt wrote:
Hi all,

If we have 8 people in a meeting, in how many ways they can sit around a table?
A) 10*9!
B) 9*8!
C) 8*7!
D) 7*6!
E) 6*5!


If there are "n" people sitting around a table, there are "(n-1)!" possible arrangements:

Here, n=8
(n-1)!=7!=7*6!

Ans:"D"
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 14 Apr 2011, 04:47
(8-1)! = 7! = 7*6!
Answer - D
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 14 Apr 2011, 07:29
1
Correct, How about when we want 2 people to sit together at any rate?
The answer may not among the choices
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 14 Apr 2011, 08:34
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saeedt wrote:
Correct, How about when we want 2 people to sit together at any rate?
The answer may not among the choices


When you have, say, 5 people, A, B, C, D and E, and you want to know how many seating arrangements are possible in a row of 5 seats, the answer is 5!; you have 5 choices for the first seat, 4 for the second, and so on. Now, if A and B must sit next to each other, the answer will be smaller. First, if A is to the left of B, then we know AB must appear together in our seating arrangement, so we can think of AB as one person; there are 4! possible arrangements. Since B might be to the left of A, there are a further 4! arrangements, and the answer would be 4! + 4! = 2*4!.

Now in the case of a circular permutation, you can use the same reasoning. Suppose you have 5 people, and 5 seats around a circular table, and you want to know how many arrangements are possible when all that matters is how the people are seated relative to each other. With no restrictions, then it makes no difference where we seat person A since we only care about the order of the people relative to each other; we then have 4 choices for who is clockwise to A's left, 3 choices for the next seat, and so on, and the answer is 4!.

Finally, to get to your question, if, say, A and B need to be next to each other, and we have 5 seats around a circle, we have two possibilities. If B is clockwise to A's left, we can think of AB as one letter. We then have 3 choices for who is clockwise next to AB, 2 choices for the next seat, and 1 choice for the final seat, for 3! arrangements. If A is clockwise to B's left, we again have 3! arrangements, for a total of 2*3! arrangements.

Finally, I'd add that circular permutation questions are rare on the GMAT (though I have seen one or two), and they need to be very precisely worded. The question in the first post above does not make clear that it is asking about circular permutations. A permutation is circular *only* when we don't care which seat each person is in - we only care who is sitting next to each other. If you have a circular table, but one seat is next to the window, and you care who gets the window seat, then the permutation is *not* circular; it's just a standard seating arrangement question in that case. A properly worded circular permutation question will always include a phrase like 'relative to each other' to make clear that the permutation is indeed a circular one.
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 14 Apr 2011, 08:59
Great explanation IanStewart,

Yes, I thought the question can imply a circular permutation, so no need for an elaborate GMAT-like permutation. thanks for the explanation
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 17 Apr 2011, 07:00
saeedt wrote:
Correct, How about when we want 2 people to sit together at any rate?
The answer may not among the choices


I think the answer would be (8-2)! x 2!(the ways to arrange two persons)=2 x 6!
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 17 Apr 2011, 13:27
for original question, if it was not circular, then 2* 8!?
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 17 Apr 2011, 21:04
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Warlock007, Excellent, 2! (to people sitting together) * 6! ((8-6)!)= 2!*6!

I'm sorry the other two answers aren't correct
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 17 Apr 2011, 23:09
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saeedt wrote:
Warlock007, Excellent, 2! (to people sitting together) * 6! ((8-6)!)= 2!*6!

I'm sorry the other two answers aren't correct


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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 19 Apr 2011, 05:11
IanStewart wrote:

When you have, say, 5 people, A, B, C, D and E, and you want to know how many seating arrangements are possible in a row of 5 seats, the answer is 5!; you have 5 choices for the first seat, 4 for the second, and so on. Now, if A and B must sit next to each other, the answer will be smaller. First, if A is to the left of B, then we know AB must appear together in our seating arrangement, so we can think of AB as one person; there are 4! possible arrangements. Since B might be to the left of A, there are a further 4! arrangements, and the answer would be 4! + 4! = 2*4!.


Hi Ian

I believe if AB are not restricted to sit together then in that case - the number of ways in which A is to the left of B is 5!/2. Similarly there are 5!/2 ways in which A is to the right of B. Can you pls confirm this?

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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 19 Apr 2011, 09:44
gmat1220 wrote:
Hi Ian

I believe if AB are not restricted to sit together then in that case - the number of ways in which A is to the left of B is 5!/2. Similarly there are 5!/2 ways in which A is to the right of B. Can you pls confirm this?


Yes that's right. If you are asked how many ways 5 people can line up so that A is somewhere to the left of B (not necessarily immediately next to B), there are 5! ways they could line up with no restrictions, and in half of those lineups A is to the left of B, and in half of those lineups, A is to the right of B, so there are 5!/2 lineups in which A is somewhere to the left of B.
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 22 Apr 2011, 14:43
Answer is D.

7! = 7*6!
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 26 Mar 2015, 04:13
saeedt wrote:
If we have 8 people in a meeting, in how many ways they can sit around a table?

A) 10*9!
B) 9*8!
C) 8*7!
D) 7*6!
E) 6*5!



Answer (8-1)! or 7*6! Answer D
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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New post 10 Jul 2016, 14:32
Circular Permutation: n!/n

Therefore, 8!/8 = 7! (or 7*6!) (D)
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Re: If we have 8 people in a meeting, in how many ways they can sit around  [#permalink]

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