Question

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

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

Answer 1

Answer: (A)

$9(10!)$

Given that there are $12$ people , they can be arranged around round table in $11!$ ways

Now consider that $2$ particular persons will sit always together , Now number of arrangements possible are $10!\times 2!=2\times 10!$

The number of arrangements in which $2$ particular persons are not to sit side by side is $11!-2\times 10!=9(10!)$

The correct option is $A$