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

Answer 1

The correct option is A $6!\times 5!$

Every alternate position must be occupied br women

$\therefore \Rightarrow 5!$

$\therefore$ arranging $6$ men on rest places $=6!$

Total no. of ways $=6!\times 5!$