Question

The number of ways in which 5 boys and 4 girls sit around a circular table so that no two girls sit together is:

• A. $5!4!$
• B. $5!3!$
• C. $5!$
• D. $4!$

Answer 1

The correct option is A $5!4!$

First all the boys are arranged in a circle, then the girls in places between the boys.
$no$ of ways of arranging 5 boys around a circle is $(5-1)!=4!$
$no$ of ways of placing 4 girls between 5 places in between boys is ${}^5{P}_4=\frac{5!}{(5-4)!}=5!$
$\therefore$ Total numbers of ways $=4!5!$