To find the number of positive integers less than 500 that can be formed using the digits 1, 2, 3, and 5, we can consider the following cases:

Case 1: 1-digit numbers (1, 2, 3, and 5) There are 4 one-digit numbers.

Case 2: 2-digit numbers We can form 2-digit numbers using the digits 1, 2, 3, and 5. These numbers can be any permutation of the digits.

Number of 2-digit numbers = 4 choices for the tens digit (1, 2, 3, or 5) × 4 choices for the units digit (excluding 0) = 4 × 4 = 16 numbers

Case 3: 3-digit numbers We can form 3-digit numbers using the digits 1, 2, 3, and 5. These numbers can be any permutation of the digits.

Number of 3-digit numbers = 4 choices for the hundreds digit (1, 2, 3, or 5) × 4 choices for the tens digit (1, 2, 3, or 5) × 3 choices for the units digit (excluding the tens digit) = 4 × 4 × 3 = 48 numbers

Now, let's sum up the numbers from all the cases:

Total number of positive integers less than 500 = Case 1 + Case 2 + Case 3 = 4 + 16 + 48 = 68

So, there are 68 positive integers less than 500 that can be formed using the digits 1, 2, 3, and 5.