Write all the possible three-digit numbers using the digits 5, 0 and 7 without repetition of the digits.

Explanation

To solve the problem of finding all possible three-digit numbers using the digits 5, 0, and 7 without repetition, we can follow these steps:

### Step 1: Identify the Digits
We have three digits to work with: 5, 0, and 7.

### Step 2: Determine the First Digit
Since we are forming a three-digit number, the first digit cannot be 0 (as it would not be a three-digit number). Therefore, the first digit can only be 5 or 7.

### Step 3: Case 1 - First Digit is 5
If the first digit is 5, the remaining digits we can use are 0 and 7. We can arrange these in the following ways:
- Second digit: 0, Third digit: 7 → Number: 507
- Second digit: 7, Third digit: 0 → Number: 570

So, from this case, we have two numbers: **507, 570**.

### Step 4: Case 2 - First Digit is 7
If the first digit is 7, the remaining digits we can use are 5 and 0. We can arrange these in the following ways:
- Second digit: 5, Third digit: 0 → Number: 750
- Second digit: 0, Third digit: 5 → Number: 705

So, from this case, we have two more numbers: **750, 705**.

### Step 5: List All Possible Numbers
Combining the results from both cases, we have the following three-digit numbers:
1. 507
2. 570
3. 705
4. 750

### Final Answer
The possible three-digit numbers using the digits 5, 0, and 7 without repetition are: **507, 570, 705, 750**.

---