A dollar bill serial number is a $10-$character string that starts with a letter from the $12$ element set

$($A$,$ B$,$C$,$ D$,$ E$,$ F$,$ G$,$ H$,$ I, J$,$ K$,$ L$\}$ followed by an $8-$digit string $($each digit from the set of $10$ digits $1,1,2,3,4,5,6,7,8,9\})$ and ending with a letter or a star from the $25$ element set:

$($A$,$ B$,$C$,$ D$,$ E$,$ F$,$ G$,$ H$,$ I, J$,$ K$,$ L$,$ M$,$ N$,$ P$,$ Q$,$ R$,$ S$,$ I, U$,$ V$,$ W$,$ X$,$ Y$,*$;

How many serial numbers contain exactly $3$ different characters:

Ex: E$10010110$E$,$ D$98989898$D$,$ H$0008000$H$,$ F $77777777$Y