Just calculate probability Egg and fur sit next to each other and subtract it from 1.

In a circle, we can arrange n people in (n-1)! ways.

First we calculate probability egg and fur sit next to each other. We can consider egg and fur as one unit for the sake of simplicity of calculation, since we are calculating cases in which they sit together.

So number of ways in which egg and fur sit next to each other in round table = ((6 - 1) - 1)! = 4!

But Egg and Fur can also sit next to each other in two ways, because when we look from Fur’s perspective, Egg can either be on his left or right. So we multiply above answer with 2, because it leads to twice the possibilities = 2 x 4!

Total number of circular seating arrangements = (n-1)! = (6-1)! = 5!

So probability of Egg and Fur sitting next to each other = (2 x 4!) / 5!

Thus, probability of Egg and Fur NOT sitting next to each other 1 - (2 x 4!) / 5! = 3/5.

Please correct me if I am wrong.