Take the task of creating three-digit numbers and break it into stages.

Stage 1: Select a digit for the hundreds position
Since the first digit cannot be 0, we must select the digit from 1, 2, 3, or 4
So, we can complete stage 1 in 4 ways

Stage 2: Select a digit for the tens position
This digit can be any digit from {0, 1, 2, 3, 4} EXCEPT the digit selected in stage 1 (to avoid repeated digits).
So, we can complete stage 2 in 4 ways

Stage 3: Select a digit for the units position
This digit can be any digit from {0, 1, 2, 3, 4} EXCEPT the two digits selected in stages 1 and 2 (to avoid repeated digits).
So, we can complete stage 3 in 3 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a three digit number) in (4)(4)(3) ways (= 48 ways)

Answer: 48