Question

A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.

Hint:

When forming a number with specific restrictions, start by considering the restricted positions first (e.g., the first digit for a number greater than a certain value) and then the unrestricted positions.

Answer 1

We are tasked with finding how many 3-digit numbers greater than 500 can be made using the digits 3, 4, 5, and 7. Step 1: Consider the first digit.
For the number to be greater than 500, the first digit must be 5 or 7, as these are the only digits from the given set that will make the number greater than 500. So, there are 2 possible choices for the first digit: \( 5 \) or \( 7 \).
Step 2: Consider the second and third digits.
For the second and third digits, we can use any of the 4 available digits (3, 4, 5, 7) because there are no restrictions. Thus, for each of the second and third digits, there are 4 possible choices.
Step 3: Calculate the total number of possibilities.
Now, multiply the number of possibilities for each digit: \[ \text{Total number of possibilities} = 2 \times 4 \times 4 = 32 \] Thus, the total number of 3-digit numbers greater than 500 that can be made with the digits 3, 4, 5, and 7 is: \[ \boxed{32} \]