Question

Select the correct answer from the given alternative

There are 10 persons among whom two are brothers. The total number of ways in which these persons can be seated around a round table so that exactly one person sits between the brothers is equal to:

Options

• 2! × 7!

• 2! × 8!

• 3! × 7!

• 3! × 8! 

Answer 1

2! × 8!

Explanation;

Exactly one person sits in between 2 brothers in 8 ways from 8 persons excluding 2 brothers.

The two brothers can change their places in ²P₂ = 2! ways.

After this, the remaining 7 persons can sit in ⁷P₇ = 7! ways.

∴ required number of ways = 8 × 2! × 7! = 2! × 8!