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# In how many ways can 5 people from a group of 6 people be se

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In how many ways can 5 people from a group of 6 people be se [#permalink]  14 May 2019, 00:41
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Question Stats:

66% (00:34) correct 33% (00:17) wrong based on 9 sessions
In how many ways can 5 people from a group of 6 people be seated around a circular table?

(A) 56

(B) 80

(C) 100

(D) 120

(E) 144
[Reveal] Spoiler: OA

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Re: In how many ways can 5 people from a group of 6 people be se [#permalink]  15 May 2019, 05:15
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In how many ways can 5 people from a group of 6 people be seated around a circular table?

To avoid using Combination or Permutation notation, you can always just consider the following steps to manually calculate the scenario:

1) Draw a ____ for each selection to be made and label any dictated restrictions for the selection.
In this case there will be a selection of five seats:
Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5

2) Insert the number or available options at moment of selection one blank at a time.
In this case: Seat 1 = 6 | Seat 2 = 5 | Seat 3 = 4 | Seat 4 = 3 | Seat 5 = 2

3) Now, for each seat consider - does order matter? If order does matter, there is no need to cancel out equivalent options, so just multiply by the number of options available for the selection. However, if order does not matter, you must first divide the number of available options by the number of equivalent available _____s at the moment of selection.

So, in this case with a circular table, in the selection of the first seat, order does not matter since the arrangement is based on the perspective of whomever is seated first regardless of where they sit. So, for seat 1 you must divide the 6 available people by the 5 available equivalent seats.

Once the perspective is established by seating the first person, however, order does matter so you must not divide the remaining available options leaving 5 x 4 x 3 x 2 for the remaining seats.

4) Finally, calculate. When selecting this AND that - multiply, but first reduce any present fractions to simplify the calculation. So, in the first seat the 6/5 can be canceled with the x 5 in seat 2, so there remain 6 x 4 x 3 x 2 = 144 ways to seat these five people from a group of six around a circular table, which matches choice E.
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Re: In how many ways can 5 people from a group of 6 people be se [#permalink]  12 Aug 2019, 07:42
Carcass wrote:
In how many ways can 5 people from a group of 6 people be seated around a circular table?

(A) 56

(B) 80

(C) 100

(D) 120

(E) 144

NEED EASY EXPLANATION
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Re: In how many ways can 5 people from a group of 6 people be se [#permalink]  14 Aug 2019, 01:51
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Five people need to choose from six people to form group. Thus, number of groups possible (using nCr formula) : 6!/5!1! = 6

Now each group consists of five people and they need to seat in circle
Therefore, using formula of (n-1)!: (5-1)! = 4! = 24

Thus, number of ways can 5 people from a group of 6 people be seated around a circular table would be 6*24 = 144.
Re: In how many ways can 5 people from a group of 6 people be se   [#permalink] 14 Aug 2019, 01:51
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