A fivefive$-$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 $232.$ If no other region has these first three digits as part of its$$ code, how many codes can exist in this$$ region?