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

$\{0,1,2,3,4,5,6,7,8,9\}$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$,$ T$,$ U$,$ V$,$ W$,$ X$,$ Y$,*\}$

a$)$How many serial numbers have all different characters?

b$)$ How many serial numbers have all different characters?