If repetition of digits is allowed, then the number of even natural numbers having three digits is

Options

A. 250
B. 350
C. 450
D. 550

Answer

To find the number of even natural numbers having three digits with repetition of digits allowed, we can follow these steps:

### Step 1: Identify the last digit
Since we are looking for even numbers, the last digit must be an even digit. The possible even digits are: 0, 2, 4, 6, and 8. This gives us a total of 5 choices for the last digit.

**Hint:** Remember that even numbers end with 0, 2, 4, 6, or 8.

### Step 2: Identify the first digit
The first digit of a three-digit number cannot be 0 (as it would not be a three-digit number). Therefore, the first digit can be any digit from 1 to 9. This gives us a total of 9 choices for the first digit.

**Hint:** The first digit must be a non-zero digit to ensure it's a three-digit number.

### Step 3: Identify the middle digit
The middle digit can be any digit from 0 to 9, which gives us a total of 10 choices for the middle digit.

**Hint:** The middle digit can be any digit, including 0.

### Step 4: Calculate the total number of combinations
Now, we can calculate the total number of three-digit even natural numbers by multiplying the number of choices for each digit together:

- Choices for the first digit: 9
- Choices for the middle digit: 10
- Choices for the last digit: 5

The total number of even three-digit natural numbers is given by:

\[ \text{Total combinations} = (\text{Choices for first digit}) \times (\text{Choices for middle digit}) \times (\text{Choices for last digit}) = 9 \times 10 \times 5 \]

Calculating this gives:

\[ 9 \times 10 = 90 \]
\[ 90 \times 5 = 450 \]

Thus, the total number of even natural numbers having three digits is **450**.

### Final Answer:
The number of even natural numbers having three digits is **450**.

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