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

$6!\times 5!$

Explanation for the correct option:

Find the required number of arrangements.

We have to arrange $6$ men and $5$ women on a round table such that no two women will sit together.

So first, arrange the men.

Since, the total number of ways in which $6$ men can be arranged on a round table is $6!$.

Now, there are $6$ empty places on the round table for the $5$ women.

So, the total number of ways in which $5$ men can be arranged on a round table is $5!$.

So, the total number of arrangements of $6$ men and $5$ women on a round table such that no two women will sit together is $6!\times 5!$.

Therefore, 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 $6!\times 5!$.

Hence, option $A$ is the correct answer.