[12 points] Let $N = \{ 1,2,3,4,5,6,7,8,9 \}$ and $L = \{ a , b , c \}$.\\
(i) Suppose we arrange the 12 elements of $L \cup N$ in a line such that no two of the three letters occur consecutively. If the order of the letters among themselves does not matter, find the number such arrangements.\\
(ii) Find the number of functions from $N$ to $L$ such that exactly 3 numbers are mapped to each of $a , b$ and $c$.\\
(iii) Find the number of onto functions from $N$ to $L$.