# 12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is: Option 1) 9(10!) Option 2) 2(10!) Option 3) 45(8!) Option 4) 10!

As learnt in concept

Conditions for Circular Permutation -

The number of circular permutations of n distinct things = (n - 1)!

-

Total permutations =$11!$

when two particular persons are together, then number of arrangements= 10!*2

Thus required cases: 11!-2*10!= (11-2)* 10!

= 9*10!

Option 1)

9(10!)

Correct option

Option 2)

2(10!)

Incorrect option

Option 3)

45(8!)

Incorrect option

Option 4)

10!

Incorrect option

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