Question

In a group of $8$ boys, two boys are brothers. The number of ways in which they can sit in a row if the brother are not to sit together is

• A. $30240$
• B. $1410$
• C. $2830$
• D. $8420$

Answer 1

The correct option is A $30240$

Number of ways in which the brothers will not sit together=Total number of ways-number of ways in which the brothers will sit together

Now,

Total number of ways$=8!=4032$

Number of ways in which the two boys will sit together is $7!$(taking the two brothers as one element ) but the two brothers can change their place

$\therefore$ Total no. of ways in which the brothers will together $=7!\times 2=10080$

$\therefore$ number of ways in which the brothers will not sit together $=40320-10080=30240$