Question

There are $20$ persons among whom are two brothers. The number of ways in which we can arrange them around a circle so that there is exactly one person between the brothers is

• A. $19!$
• B. $2\times 18!$
• C. $2!17!$
• D. None of these

Answer 1

The correct option is B $2\times 18!$

Let us fix the brothers in 2 positions

and they both can interchange

Therefore no. of ways other persons can sit will be

$\Rightarrow 2\times 18!$

Answer