The  letters of the word "ATTRACTION" are written randomly. The probability that no two T's appear together is

$\text{ Total words }=\frac{10!}{2!3!}$
$\text{ Number of words two T's appear together }=\frac{9!}{2!}-\frac{8!}{2!}$
$=\frac{8.8!}{2!}$
$\text{ Number of words no two }{T}^{\mathrm{\prime }}s\text{ appear together }$

$=\frac{10!}{2!3!}-\frac{8.8!}{2!}=\frac{21.8!}{3!}$
$\text{ Probability }=\frac{21\cdot 8!\cdot 2!\cdot 3!}{3!\cdot 10!}=\frac{7}{15}$