How many numbers greater than 1000 but not greater than 4000 can be formed with the digits 0 1 2 3 4 repetion of digits being allowed

Options

A. 374
B. 375
C. 376
D. none of these

Answer

To find how many numbers greater than 1000 but not greater than 4000 can be formed with the digits 0, 1, 2, 3, and 4 (with repetition of digits allowed), we can break down the problem step by step.

### Step 1: Determine the range of numbers
We are looking for 4-digit numbers that are greater than 1000 and less than or equal to 4000. This means the first digit (thousands place) can only be 1, 2, or 3 (since 4 would make it greater than 4000).

### Step 2: Choose the first digit
The first digit can be:
- 1
- 2
- 3

This gives us **3 options** for the first digit.

### Step 3: Choose the remaining digits
The remaining three digits (hundreds, tens, and units places) can be any of the digits 0, 1, 2, 3, or 4. Since repetition is allowed, each of these places can have any of the 5 digits.

- For the second digit (hundreds place), we have **5 options** (0, 1, 2, 3, 4).
- For the third digit (tens place), we also have **5 options** (0, 1, 2, 3, 4).
- For the fourth digit (units place), we again have **5 options** (0, 1, 2, 3, 4).

### Step 4: Calculate the total combinations
Now, we can calculate the total number of combinations by multiplying the number of options for each digit:

Total combinations = (options for first digit) × (options for second digit) × (options for third digit) × (options for fourth digit)

Total combinations = 3 × 5 × 5 × 5

### Step 5: Perform the calculation
Now we perform the multiplication:

Total combinations = 3 × 5 × 5 × 5 = 3 × 125 = 375

Thus, the total number of numbers greater than 1000 but not greater than 4000 that can be formed with the digits 0, 1, 2, 3, and 4 is **375**.