Question

In how many ways can a family of four be seated at a round table if two brothers must sit together?

Answer 1

The 4-member family can be seated in 4! ways.
The two brothers can be seated together in 2! ways.

Therefore, the total number of ways is
$\frac{4!}{2!} = \frac{4.3.2.1}{2.1} =4*3=12$

Diagrammatically, the result is shown in the figure below. The two brothers are family members 3 and 4, shown in shaded color.

Answer: 12 ways.