Question

in how many ways can 7 people be seated at a round table if 12 particular people must not sit next to each other?

Answer 1

REF. Image.

$\to$ 7 boys on a round table

$\frac{n!}{n}$ [for n boys]

$[\because$ round table]

$P_{Total}=6!$

$P_{Total}=\frac{7!}{7}$

$\to$ For 2 boys together

consider a block arrangement

$\to 5!\times 2!$ permutation

$=240$

$P_2$boys together

$\frac{6!\times 2!}{6}=P_2$ boys together

$\to$ For 2 particular boys apart,

$\Rightarrow P_{Total}-P_2$ boys together

$=6!-5!\times 2$

$=4\times 5!$

$=480$