A hexadecimal string consists of hex digits: $0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F$

a$.$ How many hex strings of length $10$ have only number digits $(0,1,2,$dots,$9)?$

b$.$ How many hex strings of length $10$ have at most $2$ letters?

c$.$ How many hexadecimal $($hex$)$ strings of length $10$ are there?

d$.$ How many hex strings of length $10$ have exactly $7$ distinct number digits in a row

$($in succession$)$ with the rest being letters?

e$.$ How many hex strings of length $10$ have at least one number digit and at least

one letter $(A,B,C,D,E,F)?$