Question

Three students $A,B,andC$ are sitting around a circular table. The probability that $AandB$ do not sit together is .

Answer 1

We know that the probability of an outcome is given by:

$P\left(E\right)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Here, $E$ is the event of $A$ and $B$ sitting together.

Let us draw the figure of their seating arrangement.

Since they are seated in a circular fashion, the order does not matter. Hence, $A,B,$ and $C$ will always sit next to each other.

$\therefore$ Number of favourable outcomes = $0$
$\Rightarrow P\left(E\right)=0$

Hence, the probability that $A$ and $B$ will not sit next to each other will be $0$.