There are 10 persons among whom two are brothers. The total number of

1.	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:(A) 2! × 7!(B) 2! × 8!(C) 3! × 7!(D) 3! × 8!
Answer» (B) 2! × 8! Select a person from 8 people (i.e., the people excluding two brothers). This is done in 8 ways. 2 brothers sit adjacent to the selected person on two sides, they may interchange their seats. Remaining 7 people sit in 7! ways Required number = 8 × 2 × 7! = 2! × 8!

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:(A) 2! × 7!(B) 2! × 8!(C) 3! × 7!(D) 3! × 8!

Answer»

(B) 2! × 8!

Select a person from 8 people (i.e., the people excluding two brothers).

This is done in 8 ways.

2 brothers sit adjacent to the selected person on two sides, they may interchange their seats.

Remaining 7 people sit in 7! ways Required number = 8 × 2 × 7! = 2! × 8!