Question

A party of $23$ persons take their seats at a round table. Find the odds against two persons sitting together .

Answer 1

$P=\frac{21!2!}{22!}=\frac{21!\times 2}{22\times 21!}=\frac{2}{22}=\frac{1}{11}=\frac{1}{1+10}$

$\therefore$Odd against$=10:1$