Understanding the Problem

We need to find the count of numbers that are strictly greater than 1000 using the digits 0, 1, 2, and 3 without allowing any digit to be repeated. Since the numbers must be greater than 1000 and we only have four digits available, the numbers formed must be exactly four digits long.

Constraints and Conditions

• Available digits: {0, 1, 2, 3}
• Repetition: Not allowed
• Number requirement: Greater than 1000 (meaning 4-digit numbers)
• First digit cannot be 0 for a 4-digit number.

Step-by-Step Calculation

We will determine the number of choices for each digit position (thousands, hundreds, tens, units) starting from the most significant digit.

1. Thousands Place: The number must be greater than 1000, so the thousands digit cannot be 0. The possible choices are 1, 2, or 3. Number of choices = 3.
2. Hundreds Place: After selecting the thousands digit, three digits remain. The hundreds digit can be any of these remaining digits (including 0). Number of choices = 3.
3. Tens Place: Two digits have been used. The tens digit can be chosen from the remaining two digits. Number of choices = 2.
4. Units Place: Only one digit remains after filling the first three places. Number of choices = 1.

Total Number of Combinations

To find the total number of distinct numbers greater than 1000 that can be formed, we multiply the number of choices for each position.

Total numbers = (Choices for thousands) \(\times\) (Choices for hundreds) \(\times\) (Choices for tens) \(\times\) (Choices for units)

Total numbers = \(3 \times 3 \times 2 \times 1\)

Total numbers = 18

Conclusion

Therefore, there are 18 distinct numbers greater than 1000 that can be formed using the digits 0, 1, 2, and 3 without repetition.