The number of 3 digit natural numbers less than 5,00 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to

Options

A. 100
B. 20
C. 80
D. 50

Answer

To find the number of three-digit natural numbers less than 500 that can be formed using the digits 0, 1, 3, 7, and 9 (with repetition allowed), we can follow these steps:

### Step 1: Identify the digits and constraints
The available digits are: 0, 1, 3, 7, 9.
Since we are forming a three-digit number that must be less than 500, the first digit (hundreds place) cannot be 0, 7, or 9.

### Step 2: Determine possible digits for the first position
The first digit must be either 1 or 3 to ensure the number is a three-digit number and less than 500. Thus, we have:
- Possible choices for the first digit: 1, 3 (2 options).

### Step 3: Determine possible digits for the second position
The second digit can be any of the available digits (including 0). Thus, we have:
- Possible choices for the second digit: 0, 1, 3, 7, 9 (5 options).

### Step 4: Determine possible digits for the third position
Similar to the second digit, the third digit can also be any of the available digits. Thus, we have:
- Possible choices for the third digit: 0, 1, 3, 7, 9 (5 options).

### Step 5: Calculate the total number of combinations
Now, we can calculate the total number of three-digit numbers that can be formed:
- Total combinations = (Choices for the first digit) × (Choices for the second digit) × (Choices for the third digit)
- Total combinations = 2 (for the first digit) × 5 (for the second digit) × 5 (for the third digit) = 2 × 5 × 5 = 50.

### Final Answer
The total number of three-digit natural numbers less than 500 that can be formed is **50**.

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