Question

The number of 3-digit numbers greater than 500, that can be formed using the digits 3, 4, 5, and 7, with repetition, is

• A. 32
• B. 16
• C. 18
• D. 12
• E. 24

Hint:

Always start with the constraint (Hundreds place must be \(>4\)). Since repetition is allowed, all other slots simply take the full count of available digits.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We need to form a 3-digit number using the set {3, 4, 5, 7} such that the number is greater than 500. Repetition of digits is allowed.

Step 2: Key Formula or Approach:
Fundamental Principle of Counting (Multiplication Rule).

Step 3: Detailed Explanation:
Let the 3-digit number be represented by slots: [Hundreds] [Tens] [Units].
1. Hundreds place: To be greater than 500, the first digit must be 5 or 7.
Number of choices = 2 (Digits: 5, 7).
2. Tens place: Any of the given digits {3, 4, 5, 7} can be used since repetition is allowed.
Number of choices = 4.
3. Units place: Any of the given digits {3, 4, 5, 7} can be used.
Number of choices = 4.
Total numbers = (Choices for Hundreds) \(\times\) (Choices for Tens) \(\times\) (Choices for Units)
\[ \text{Total} = 2 \times 4 \times 4 = 32 \]

Step 4: Final Answer:
The total number of such 3-digit numbers is 32.