(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

6 children are sitting arounbd a round table, with each chair numbered from 1 to six. In how many ways can we rearange them so that no child sits across from the child who was across him before.

2. Relevant equations

3. The attempt at a solution

Because the chairs are numbered it makes a difference where each child sits.

To seat the 1st child, A, we have 6 options, and 5 open seats remain.

To seat the child that previously sat across from A, A', we have 4 options. And 4 seats remain

To seat the 3rd child, B, we have 4 options, and 3 open seats remain.

To seat the child that previously sat across from B, B', we have 2 options. And 2 seats remain

To seat the 5th child, C, we have 2 options, and 1 open seats remain.

To seat the child that previously sat across from C,C', we have 1 option.

Notice that by the way we sat the other children, C and C'can not be across from each other.

in total there are 6*4*4*2*2= 384.

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# Combinatorics, is this correct

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