Question

The number of ways in which $7$ people can be arranged at a round table so that $2$ particular persons must not sit together, is

• A. $132$
• B. $148$
• C. $480$
• D. $noneofthese$

Answer 1

The correct option is C $480$

Total no. of ways in which $7$ people can be arranged $=(7-1)!=6!$

Taking $2$ as the unit,

$\Rightarrow (6-1)!\times 2!=5!\times 2!$

$\therefore$ Total no. of ways in which $7$ can be arranged that two particular persons must not sit together $=6!-5!2!$

$=720-240$

$=480$

Hence, the answer is $480.$