Among all ordered pairs $( x , y , z )$ of non-negative integers satisfying the equation $x + y + z = 10$, one is randomly selected. Find the probability that the selected ordered pair $( x , y , z )$ satisfies $( x - y ) ( y - z ) ( z - x ) \neq 0$. If this probability is $\frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]