Problem #PRU-100549

Problem

A palindromic number is a number that reads the same backward and forward. (For example, $13531$ is palindromic.)

a) How many $5$-digit numbers are palindromic?

b) How many $5$-digit numbers are palindromic and consist of distinct digits?

c) How many $5$-digit numbers consist of $3$ distinct digits and end with 2?

d) How many $5$-digit numbers are odd and consist of $3$ distinct digits?