Permutation Problem: Sitting in a Circle/Table

Arrangements in a circles: This video will take you through finding the total possible arrangement of n people in a circle or at a table.

[AnshikaJindal-ge]

Thank you! That was really helpful. It helped us solve a maths challenge!

[lebaguette]

Suppose that you were sitting down at this table. The napkins are in front of you, which napkin would you take? The one on your ‘left’? Or the one on your ‘right’? The one on your left side? Or the one on your right side? Usually you would take the one on your left side. That is ‘correct’ too. But in a larger sense on society, that is wrong. Perhaps I could even substitute ‘society’ with the ‘Universe’. The correct answer is that ‘It is determined by the one who takes his or her own napkin first.’ …Yes? If the first one takes the napkin to their right, then there’s no choice but for others to also take the ‘right’ napkin. The same goes for the left. Everyone else will take the napkin to their left, because they have no other option. This is ‘society’… Who are the ones that determine the price of land first? There must have been someone who determined the value of money, first. The size of the rails on a train track? The magnitude of electricity? Laws and Regulations? Who was the first to determine these things? Did we all do it, because this is a Republic? Or was it Arbitrary? NO! The one who took the napkin first determined all of these things! The rules of this world are determined by that same principle of ‘right or left?’! In a Society like this table, a state of equilibrium, once one makes the first move, everyone must follow! In every era, this World has been operating by this napkin principle. And the one who ‘takes the napkin first’ must be someone who is respected by all. It’s not that anyone can fulfill this role… Those that are despotic or unworthy will be scorned. And those are the ‘losers’. In the case of this table, the ‘eldest’ or the ‘Master of the party’ will take the napkin first… Because everyone ‘respects’ those individuals.”

[princessbinaban]

thank you that was really helpful and i learned a lot

[godwintakyi]

In how many ways can six players be lined if two particular
Players must not stand next two each other.

[shambhavi]

Thanks..the explanation was really helpful!

[rockyshepheard]

I would like to argue that the number of ways to sit around a table is exactly the same as the number of ways to sit in a line. In a line you could have A, B, C, D, E. A is effectively sitting next to E (as in the circle). It’s just that line circle A and E have been pulled apart by a small distance. It certainly cannot be that statistics is based on slight differences in proximity, could it? If in the circle scenario, you move any two seats apart by even a small distance you no longer have a circle but you now have established a curved line...and oddly have changed number of ways from 24 to 120 by this simple displacement. I hate that there needs to be any more than two equations nPr and nCr to solve any comb/perm question, so, I am seeking the barest-bones generalizations that will allow the previous two equations to be sufficient to solve any comb/perm work problem. I am very interested in your thoughts on this. Thank you!

[mirrokonuddin]

I have a question.. If Two students of pharmacy disparment can not be seated together, how many ways 5 students of chamisry and 5 students of pharmacy can be seated?

[mashalsana]

What about when we have to arrange 6 keys in a keychain ?

[samarth]

Any chance this applies to champagne glasses at a wedding?

[vianneygarcia]

10. How many ways can 12 students line up in 10 positions if the third and fourth position must be student x or y?

[satvikkumarpatel]

Why do we divide by 5 and not subtract 5?

[mrkakazvlog]

this is my Question [In how many ways can 7 boys be seated at a round table so that two particular boys are separated?]

[ranahassanali]

i have a question that in how many ways five men and five women can be seated around a round table such that nobody of same sex sit together (sit alternatively)