Question

The number of ways in which we can arrange n ladies & n gentlemen at a round table so that $2$ ladies and $2$ gentlemen may not sit next to one another is:

• A. $\left(n-1\right)!\left(n-2\right)!$
• B. $\left(n!\right)\left(n-1\right)!$
• C. $\left(n+1\right)!\left(n\right)!$
• D. None of these

Answer 1

Answer: (B)

$\left(n!\right)\left(n-1\right)!$

To Satisfy given condition First we have to arrange n men around the table

No of ways to do so,

$=(n-1)!$

Now, when these men are arranged and seated then there are n spaces between each men where we will arrange and seated n woman

No of ways to do so,

${=}^n{C}_n\left(n\right)!$

Hence, Total number of ways will be

$(n-1)!n!$