Five Americans, three Italians and six French sit randomly in a round table such that each sits together with their countrymen. How many seating arrangements are possible?

Question

lgbasallote · Answer

would it be 5!3!6!

lgbasallote · Answer

i think that would be how it would be if they were in a row....

lgbasallote · Answer

so maybe the two ends of the row would have the same nationality?

anonymous · Answer

am i making u nervous by watching you lol

lgbasallote · Answer

not really..no...

lgbasallote · Answer

you do make me creeped out though....

anonymous · Answer

its in a cirlce so you have to restrict..different than in a row

lgbasallote · Answer

...but 5!3!6! is for the row right?

lgbasallote · Answer

ahh i got it

4!3!6! + 5!2!6! + 5!3!5!

anonymous · Answer

for the row?

lgbasallote · Answer

circle

lgbasallote · Answer

hmm no that's not it

anonymous · Answer

hmm..i dont think that it is that easy.

anonymous · Answer

okay so you have to fix one person first..then arrange the others

lgbasallote · Answer

that's why i used what i wrote a while ago...

anonymous · Answer

but it didnt look right..hang on..lemme try

lgbasallote · Answer

yes it wasn't

lgbasallote · Answer

it's too small

lgbasallote · Answer

it's not 5!3!6! + 4!3!6! + 5!2!6! + 5!3!5! either

lgbasallote · Answer

the number of ways to arrange n objects in a circle is (n-1)!

anonymous · Answer

i think you have to do it in cases.

that is correct...but your question you have to arrange the 3 nationalities hmm..

lgbasallote · Answer

i think this is more difficult than how i make it out to be

anonymous · Answer

do they alternate?

lgbasallote · Answer

i don't think so

anonymous · Answer

like AAIIFF..
or AAAIIIFFF

lgbasallote · Answer

i now have no idea how to do this

hartnn · Answer

taking each nationality group as 1 entity , those 3 entities can be arranges in 2! ways(in circle) , so wouldn't it be simply  2!(5!3!6!)

lgbasallote · Answer

....that's right.....

lgbasallote · Answer

what did you do?

lgbasallote · Answer

explain what happened please @hartnn

hartnn · Answer

lol! 
i think u understand how n people can be arranged in (n-1)! ways in circular fashion.....or u need to understand that ?

lgbasallote · Answer

i assume it's because one can sit on the top and then (n-1)! is the permutation the others can sit on the remaining seats

hartnn · Answer

on the top ??
take 3 people,  how many ways can they sit in circular fashion ? 2 ? or more ?|dw:1348727561739:dw|