How many 3-digit numbers can you form by using the digits 6,0,8 each only once ?

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find out how many 3-digit numbers can be formed using the digits 6, 0, and 8, each only once, we need to consider the rules of forming a 3-digit number. Here’s a step-by-step solution:

### Step 1: Identify the digits
The available digits are 6, 0, and 8.

### Step 2: Determine the hundreds place
A 3-digit number cannot start with 0. Therefore, the hundreds place can only be filled by either 6 or 8.

### Step 3: Case 1 - Hundreds place is 6
- If 6 is in the hundreds place, the remaining digits are 0 and 8.
- The possible combinations for the tens and units places are:
- Tens place: 0, Units place: 8 → Number formed: 608
- Tens place: 8, Units place: 0 → Number formed: 680

So, from this case, we can form the numbers: **608, 680**.

### Step 4: Case 2 - Hundreds place is 8
- If 8 is in the hundreds place, the remaining digits are 6 and 0.
- The possible combinations for the tens and units places are:
- Tens place: 6, Units place: 0 → Number formed: 860
- Tens place: 0, Units place: 6 → Number formed: 806

So, from this case, we can form the numbers: **860, 806**.

### Step 5: Combine results
Now, we combine the results from both cases:
- From Case 1: 608, 680
- From Case 2: 860, 806

### Final Count
Thus, the total number of 3-digit numbers that can be formed is **4**.

### Summary
The 3-digit numbers that can be formed using the digits 6, 0, and 8 are:
1. 608
2. 680
3. 860
4. 806