Permutations 3

Question

Problem: people around a table
Level: Easy/Medium

In how many ways can five people sit around a circular table?
1. without any restrictions
2. one should not have the same neighbours in any two arrangements

rohansherry · Answer

IMO D: but will wait for some one to actually explain the solution

CasperMonday · Answer

This is not a data sufficiency question, Rohansherry))

rohansherry · Answer

Oppssssssss.....But i was right...if it were an DS ques the ans would be D .....

1) when there is no restriction........

We have to fix one and rotate other 4 ...

so it would be (n-1)! = 4! = 24 ans

rao · Answer

1. (5-1)! Medium to high
2. Certianly High. ans - 18

rohansherry · Answer

can you explain the second part

rao · Answer

Theres a trick to it:

For every possible arrangement you will see that a counter arrangement is also possible, consider filling 3 spots out of 5:

_, A, B, C, _
 _, C, B, A, _

So if you try to visualize this in a circle, you'll see that out of these arrangements, half would be counter-clockwise equivalent to the other half.

Since we are asked - one should not have the same neighbours - consider only one direction i.e 24/2 = 12 ways.

EDIT - my previous post had typo, the correct ans is 12.

Aleehsgonji · Answer

The answer for second part is 2 and the possible combinations are
1)ABCDE
2)ACEBD

As the people are sitting around a circular table, neighbours for A in first case are B and E.
In the second scenario it is D and C. As there are only 5 people any person will have 4 persons as neighbours as that will be covered in two scenarios. So the answer is 2

LenaA · Answer

Thanks for the clockwise explanation. Very good one.

CasperMonday · Answer

Guys, here is the OA:

1. In circular arrangements, we are not interested in actual positions of things, but rather in relative positions. Therefore, when we consider number of ways in circular arrangements, we fix one thing and rotate the others relatively to the first one. So, in this problem the solution is  (5-1)!=4!=24 
2. I only know the official answer for the second part of the problem. But, truely, I don't fully understand the concept behind it: the answer is  \frac{(5-1)!}{2}=12 . If anyone could explain it to me dummy in simple words, I would appreciate that a lot.

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rao · Answer

you can take a look at my explanation ... hope it help...

CasperMonday · Answer

Ah, alright, I see. Thank you!

Aleehsgonji · Answer

Can any one write down all the possible combinations for resticted scenario as I am can see only 2 possible combinations.
1)ABCDE
2)ACEBD

Permutations 3

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