Australian AMC 2013 - Senior Question 16

Question 16

Three darts are thrown at the $3\times3$ grid, each landing in a different small square. After each throw, each of the remaining small squares is equally likely to be hit.

Question illustration

What is the probability that the squares in which they land form a horizontal, vertical or diagonal row?

$\frac1{63}$
$\frac2{21}$
$\frac19$
$\frac1{42}$
$\frac8{81}$