A five$-$digit code is used to distinguish between different regions. The code uses numbers between $1$ and $6,$ inclusive

a$.$ How many different codes are available for use? $($Assume that any five$-$digit number can be used as a code.$)$

b$.$ The first three digits of a code for a particular region are $222.$ If no other region has these first three digits as part of its code, how many codes can exist in this region?

a$.$ The number of possible codes is $.$

$($Type an integer. Simplify your answer.$)$