The question asks how many different 3-digit numbers can be made from the cards shown, which contain the digits: 3, 4, 5, 7, and 8.

Key Information:

• You have 5 digits: {3, 4, 5, 7, 8}.
• You're required to form 3-digit numbers.

Explanation:

If digits can repeat, you would have 5 choices for each of the 3 positions in the number, leading to: $5 \times 5 \times 5 = 125 \quad \text{(if repetition is allowed)}$

If digits cannot repeat, you would have:

• 5 choices for the first digit,
• 4 remaining choices for the second digit,
• 3 remaining choices for the third digit.

So, the number of possibilities without repetition is: $5 \times 4 \times 3 = 60 \quad \text{(if repetition is not allowed)}$

The answer depends on whether repetition is allowed. Based on standard assumptions, if no specific instruction is given, we typically assume repetition is not allowed, so the answer would be 60 different 3-digit numbers.

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Related Questions:

1. How many 4-digit numbers can be formed from these cards if repetition is allowed?
2. What is the total number of even 3-digit numbers you can form if digits can repeat?
3. How many 3-digit numbers can be formed if the number must be greater than 500?
4. How many 2-digit numbers can be formed using the same digits without repetition?
5. What is the probability of randomly picking a 3-digit number divisible by 5 from these digits?

Tip:

When forming numbers from a set of digits, always check if repetition is allowed, as it significantly affects the number of possible combinations.