AMC 12 2002b Problem 1

The arithmetic mean of the nine numbers in the set $\{9, 99, 999, 9999, \ldots, 999999999\}$ is a $9$-digit number $M$, all of whose digits are distinct. The number $M$ does not contain the digit

$\mathrm{(A)}\ 0 \mathrm{(B)}\ 2 \mathrm{(C)}\ 4 \mathrm{(D)}\ 6 \mathrm{(E)}\ 8$