Six people are asked to sit down in a circle consisting of eight chair

Question

Six people are asked to sit down in a circle consisting of eight chairs.How many different ways are there to distribute the six people on the eight chairs?

A. 120
B. 720
C. 2,520
D. 5,040
E. 20,160

gvij2017 · Accepted Answer

In circular arrangement, first person always has 01 option because all chairs are same for him and position of chair doesn't matter to him.

So remaining 5 people have 7 options and for all 5, position with respect to first changes in every arrangement.

7c5* 5! is correct answer.
C is correct.

NCRanjan · Answer

First Person has 8 options , 2nd has 7 options and so on 
sp 8x7x6x5x4x3 = 20160

IMO E

ShankSouljaBoi · Answer

Hi, the first person will not have 8 options but one(Since the chairs are not numbered and when that person does actually take the sseat, then and only then the numbering is done).

NCRanjan · Answer

Well i sure did not understand the 5! part but i did understand the following

First Of the insight that the first person will have 01 option helped me a lot so thanku

Starting with this

first person - 1 choice
second - 7 
Third - 6

and so on 
so 1 x7x6x5x4x3 = 2520 (the answer)

theunicornbuzz · Answer

The thought process matters a lot in this question. Your approach will change how you solve it.

One way is to think that 6 people are arranged in a circle = 5!
Now we need to place two chairs between these 6 people
This can be done in one of these two ways:
1. Both chairs between two individuals seated in a circle = 6C1 
2. Or two chairs placed separately between these 6 seated individuals = 6C2

Hence the number of ways this can be done is = 5!(6C1 + 6C2) = 5! * 21 = 2520

hr1212 · Answer

One interesting easy way to solve this could be -

Let's start with what we know - For n people to sit in a circle with n chairs, total number of combinations are (n-1)!

Now here, we see that we have 2 extra chairs. Let's suppose 2 identical holograms are going to occupy these chairs, then number of ways to arrange 8 people in a circle where 2 of them are identical can be,

7!/2! = 5040/2 = 2520

IMO: C

Six people are asked to sit down in a circle consisting of eight chair

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GMAT Problem Solving (PS) Questions

Six people are asked to sit down in a circle consisting of eight chair

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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