How many three digit numbers can be formed by using the digits, 0,1,2,3 (repetition of digits is allowed)

Answer

To solve the problem of how many three-digit numbers can be formed using the digits 0, 1, 2, and 3 (with repetition allowed), we can follow these steps:

### Step 1: Identify the places in a three-digit number
A three-digit number has three places:
- Hundreds place
- Tens place
- Units place

### Step 2: Determine the options for the Hundreds place
The hundreds place cannot be 0 (as it would not be a three-digit number). Therefore, the valid digits for the hundreds place are 1, 2, and 3. This gives us:
- Options for the hundreds place = 3 (1, 2, or 3)

### Step 3: Determine the options for the Tens place
The tens place can be filled with any of the four digits (0, 1, 2, or 3). Therefore, we have:
- Options for the tens place = 4 (0, 1, 2, or 3)

### Step 4: Determine the options for the Units place
Similar to the tens place, the units place can also be filled with any of the four digits (0, 1, 2, or 3). Therefore, we have:
- Options for the units place = 4 (0, 1, 2, or 3)

### Step 5: Calculate the total number of three-digit numbers
To find the total number of three-digit numbers, we multiply the number of options for each place:
- Total = (Options for hundreds place) × (Options for tens place) × (Options for units place)
- Total = 3 × 4 × 4

### Step 6: Perform the multiplication
Calculating the total:
- Total = 3 × 4 × 4 = 3 × 16 = 48

Thus, the total number of three-digit numbers that can be formed using the digits 0, 1, 2, and 3 (with repetition allowed) is **48**.

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