Question

how many ways can 8 people be seated at a round table if two people refuse to sit next to each other? CIRCULAR PERMUTATION HELP

Answer 1

i'm not sure to set this up at \[\frac{ 8! }{ 8 } \] or as

8!

because it is in reference to a point?

Answer 2

@jim_thompson5910

Answer 3

@ganeshie8

Answer 4

When dealing with circles, and placing n people around them, there are (n-1)! ways do that (order matters)

Answer 5

What I would do is count the number of ways to have the two people together and then subtract it from the total number of ways to arrange the people around the table

Answer 6

are there only two ways those two people can sit next to each other though? once on the left and the other on the right?

Answer 7

that "2" is part of it

Answer 8

not the full story though

Answer 9

i said 7! - 5! is that correct. because the 8 to begin with and then subtract the other two and that leaves me with 6. six in a circular arrangement in 5! yes?

Answer 10

you have (8-1)! = 7! ways to arrange the 8 people around the table

Answer 11

let's say we had the following people: A,B,C,D,E,F,G,H

and let's say A and B don't want to be near each other. If we combine A and B together, to get Z, we get Z,C,D,E,F,G,H

arranging these 7 people gives (7-1)! = 6! ways

but like you said, there are 2 ways for each arrangement (either AB or BA) so there are really 2*6! ways

Answer 12

subtract to get 7! - 2*6!

Answer 13

that makes more sense!

Answer 14

I'm glad it does