Permutation (1 Viewer)

[Pocatello]

5 rectangular tables are arranged in a circle, each table seats three people on the long side. How many arrangements are possible if people(15 in total) may sit on the outside or inside of the circle?

Thanks

 

[damo676767]

³⁰P₁₅/15

 

[Pocatello]

Why divide by 15?

 

[SeDaTeD]

Hmm i would say 15!*2^15/5, because 15! is ibvious for all perms in a line, the 2^15 because each has either a choice of inside or outside, and the divide by 5 because you can rottae tables.

Edit: Hld on, on each table can you seat 3 or 6 people? if it's 3 then it'd be my answer. If it's six then it's 30!/(15!*5)

 

[Stefano]

If each table seats 3 on the long side I would of thought that the tables would seat 8 people:

.... _1__2__3
8 {________}4
..... 7 .. 6.. 5

 

[damo676767]

each table can sit 6

beacuse 3 on each side and then ends are blocked by the ends of other tables



and poctello i divide by 15 beacuse it is in a circle

 

[Stefano]

³⁰P₁₅/15

Could you explain your logic please?

³⁰P₁₅ ---> why ?

/15 ---> Because its a circle!? so ?

 

[SeDaTeD]

You should divide by 5, since shifting everyone along one will not get an equivalent arrangement, but shifting everyone to the next table will.