Question

The number of ways in which seven person can be arranged at a round table if two particular person may not sit together is

• A. $480$
• B. $120$
• C. $80$
• D. none of these

Answer 1

Answer: (A)

$480$

Solution:- (A) $480$

As we know that no. of ways '$n$' people can be seated around a round table $=(n-1)!$

$\therefore$ No. of ways '$7$' people can be seated around a round table $=(7-1)!=6!=720$

Now, no. of ways if two particular person (out of $7$) sit together $=5!\times 2=240$

$\therefore$ No. of ways $7$ people can be seated around a round table if two particular person can not sit together $=720-240=480$

Hence the correct answer is $480$.