Question

In a party $12$ persons are to be seated in a round table. If two particular persons are not to sit side by side, then the total number of arrangements is

• A. $9\times 10!$
• B. $2\times 10!$
• C. $45\times 8!$
• D. $10!$

Answer 1

The correct option is A $9\times 10!$

Let us assume that $2$ particular persons are sitting side by side , then the number of arrangements possible are $10!\times 2$

Total number of arrangements possible with $12$ persons in a round table are $11!$

Therefore the number of arrangements possible such that $2$ particular persons are not to sit side by side is $11!-2\times 10!=9\times 10!$

Therefore the correct option is $A$