How many whole numbers less than 500 can be formed using the digits 1, 2, 4, and 5?

We do casework by the number of digits in the number.

One-digit numbers: 4 choices for the number.

Two-digit numbers: Four choices for the first digit, four for the second, for a total of 4*4=16 numbers.

Three-digit numbers: Five cannot be the first digit, since if that is the case we will have a number over 500, so we have three choices for the first digit and four for each of the others, for a total of 3*4*4=48 numbers.

This is a total of 4+16+48=68 numbers.