Numbers using digits 0, 1, 2, 3, 4, and 5 greater than 3000 without repetition:

To determine the number of possible numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5, greater than 3000 without repetition, we can break down the problem into separate cases.

Case 1: Thousands digit is 3, 4, or 5:
In this case, the thousands digit can only be either 3, 4, or 5. The remaining digits can be any of the remaining 5 digits (0, 1, 2, 3, 4, or 5).

- For the thousands digit, we have 3 options (3, 4, or 5).
- For the hundreds digit, we have 5 options (0, 1, 2, 3, or 4).
- For the tens digit, we have 4 options (0, 1, 2, or 3).
- For the units digit, we have 3 options (0, 1, or 2).

Therefore, the total number of numbers in this case is: 3 x 5 x 4 x 3 = 180.

Case 2: Thousands digit is 2:
In this case, the thousands digit can only be 2. The remaining digits can be any of the remaining 5 digits (0, 1, 3, 4, or 5).

- For the thousands digit, we have 1 option (2).
- For the hundreds digit, we have 5 options (0, 1, 3, 4, or 5).
- For the tens digit, we have 4 options (0, 1, 3, or 4).
- For the units digit, we have 3 options (0, 1, or 3).

Therefore, the total number of numbers in this case is: 1 x 5 x 4 x 3 = 60.

Total number of numbers:
To find the total number of numbers, we need to sum up the numbers from both cases.

Total number of numbers = Numbers in Case 1 + Numbers in Case 2
Total number of numbers = 180 + 60
Total number of numbers = 240

Therefore, there are 240 numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5, greater than 3000 without repetition.

3*5*4*3