Permutation Problem: Sitting in a Circle/Table

[@Edddardd]

That was really helpful .. Thanks!

[@AnshikaJindal-g4e]

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

[@shambhavi1191]

Thanks..the explanation was really helpful!

[@princessbinaban5967]

thank you that was really helpful and i learned a lot

[@lebaguette5393]

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.”

[@Rad-c6e]

thank u so much really helpful

[@uroosaimtiaz]

Thank you for making this!

[@ireneolipendo5523]

Thank you so much. Big help indeed.

[@MrFrazerz]

Tis the season of Christmas

[@johndaveparedes1570]

thank you it was direct to the point

[@erwinlorenzo238]

Thank you Mr. Barnes

[@godwintakyi832]

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

[@mohinibarrett3347]

That was helpful

[@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?

[@jacobmate1537]

Spell properly bro

[@dimashkieahmad4065]

5! x 6 x 5 x 4 x 3 x 2

[@mashalsana4186]

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

[@samarth2808]

Any chance this applies to champagne glasses at a wedding?

[@hainamvu8918]

Thank you

[@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?]

[@ladyj9655]

@@MatsGadajevIBAKAGY I humbly disagree. I think the answer is 480 The answer you have provided is the arrangement assuming two boys are sitting together.

[@tsukkyhime]

@@ladyj9655 can u tell me the working to the answer?

[@ladyj9655]

@@tsukkyhime I hope my answer is actually correct first lol.

[@tsukkyhime]

@@ladyj9655 ah i see...well i saw this video first and looked at the comment so i asked u the working wondering if u know how...then i stumbled upon this video kzbin.info/www/bejne/rqPCl6CggNSqrK8 and based on this calculation i guess it is 5!×2! which is 240 😄😄

[@moustafakhalil5385]

@@ladyj9655 480 is the correct answer. first we try to find the possible ways where 2 boys sit together and that is 2!(the boys can interchange positions)*5! (the remaining 5 boys can interchange positions too)=240, we have the total possible ways = 720. Since two boys not sitting to each other is the opposite to two boys sitting to each other => n= total-opposite=720-240=480.

[@vianneygarcia3043]

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

[@hufficag]

12P10 divided by 12 and 11 to lock in those students who must stand in those positions

[@ranahassanali765]

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) ?????

[@sstefan1284]

@james matthews why didn't you divide all the men permutations with the number of the same seatings like you did with women? it should be 4!*4!

[@satvikkumarpatel1129]

Why do we divide by 5 and not subtract 5?

[@lowzyyy]

Lets see an example: He took one permutation ABCDE. He also showed that we have 5 times the same permutation by just rotating around the table. But he only showed one VALID permutation. For every valid permutation lets say ABCED we can rotate 5 times and get the same ABCED permutation. So in the end because we want number of VALID different permutations, we divide n! by n (in our example 5! divide 5 because EVERY different permutation ca be rotated 5 times) so we can get number of different permutation. Hope this helps

[@satvikkumarpatel1129]

@@lowzyyy thank you

[@testingsomething5280]

@@lowzyyy If you're still here, why do you divide by 5 and not 4? Shouldn't one of the 5 repetitions be valid?

[@kervinbersabe583]

Is this is curculat permutation?

[@djg2008]

thxs

[@rockyshepheard6054]

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!

[@akshattiwari8280]

You could rotate the circle and it would be the same thing.

[@TotalVikingPower]

It is a very valid point. It depends on your definition what is a unique/new arrangement. Is your unique arrangement based on the people combination or people combination incl. their placement 1. you can look only at the combination between the people then it is 120. 2. or you can choose to look at the chairs as 1,2,3,4,5,6, as well. Then every time your small circle moves one chair around that is then a new arrangement. Speaking of people sitting around a table 1. is the way to look at it generally unless you got equal number of unique individual chairs :/ Essentially people care who they sit next to, not what they sit on.

[@Ty1er]

THANKS

[@ystechzone174]

Tnx

[@minashehata6839]

Thx 😘

[@luizfarias5775]

thx

[@chesterhorca9262]

thankssssssssssssssssssssssssssssssssssssssssssssssssss

[@jonathanattards]

E-