Question

$12$ persons are to be arranged at a round table . If two particular persons among them are not to be side by side, the total number of arrangements is?

• A. $9(10!)$
• B. $2(10!)$
• C. $45(8!)$
• D. $10!$

Answer 1

The correct option is A

$9(10!)$

Explanation for the correct option:

The number of ways of arrangement of $12$ people around round table $=11!$

The number of arrangement in which two particular persons are side by side around round table $=10!(2!)$

Therefore, Total required arrangements$$\begin{gathered} =11!-10!(2!) \\ =10!(11-2) \end{gathered}$$

$=\mathbf{9}\mathbf{}\mathbf{(}\mathbf{10}\mathbf{!}\mathbf{)}$

Hence, Option ‘A’ is Correct.