With the digits 0, 5, 7, 3, 2, how many three-digit numbers can I make that are accepted on 25 parts? Repetition is allowed.


You are asking how many three-digit numbers can be made using the digits 0, 5, 7, 3, and 2 such that these numbers are divisible by 25. Let's break this problem down step-by-step:

### Condition for Divisibility by 25:
A number is divisible by 25 if its last two digits form a number divisible by 25. The two-digit combinations divisible by 25 are:
- 00
- 25
- 50
- 75

Thus, the last two digits of your three-digit number must be one of these combinations.

### Choices for the First Digit:
The first digit cannot be zero, since we're looking for a three-digit number. So, the first digit must be chosen from the set {5, 7, 3, 2}.

### Step-by-step analysis:
- For the last two digits, there are 4 possibilities: 00, 25, 50, and 75.
- For the first digit, there are 4 possible choices: 5, 7, 3, and 2.

### Total number of three-digit numbers:
Since we have 4 choices for the first digit and 4 choices for the last two digits, the total number of three-digit numbers divisible by 25 is:

\[
4 \times 4 = 16
\]

Thus, you can form **16 three-digit numbers** that are divisible by 25.

Would you like more details or have any questions?

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Here are 5 related questions:
1. How many two-digit numbers divisible by 25 can you form with the digits 0, 5, 7, 3, 2?
2. What if repetition of digits was not allowed—how many such three-digit numbers could be formed?
3. How many four-digit numbers divisible by 25 can be formed with the same digits?
4. What are the largest and smallest three-digit numbers you can make under the same conditions?
5. How would the answer change if the set of digits included 8 as well?

**Tip**: Always check the divisibility rules for numbers before solving, as they can simplify your calculations.

With the digits 0, 5, 7, 3, 2, how many three-digit numbers can I make that are accepted on 25 parts? Repetition is allowed.

Learn how to calculate the number of three-digit numbers divisible by 25 using the digits 0, 5, 7, 3, and 2. Understand divisibility rules and combinations, including detailed steps for forming numbers and exploring the rule for divisibility by 25. Suitable for students in Grades 6-8.

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