Question

The number of ways in which six men and five 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 $6!\times 5!$

The number of ways in which six men can be arranged around the table is (6 - 1)!
Now the women can be arranged in 6 gaps in 6! ways.

Hence, the total number of ways is $6!\times 5!$