Question

The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by

• A. $30$
• B. $5!4!$
• C. $7!5!$
• D. $6!5!$

Answer 1

The correct option is D $6!5!$

Total number of ways of placing $6$ men at a round table $A$ is $5!$ [Using circular permutation property]

Total number of ways of placing women in between them: $1\times 6!$
$\therefore$ Total ways are $5!\times 6!$