With the digits 0, 1, 2, 3, 4, 5, 6 and 7, even 3-digit numbers can be written by repeating the digits so that even and hundreds are greater than one.

To form even three-digit numbers using the digits \(0, 1, 2, 3, 4, 5, 6, 7\), with the conditions that the hundreds and tens digits are greater than 1 and that repetition of digits is allowed, we can proceed step by step.

### Step 1: Hundreds place
The hundreds digit must be greater than 1, so it can be any of the digits \(2, 3, 4, 5, 6, 7\). Thus, there are 6 choices for the hundreds place.

### Step 2: Tens place
Similarly, the tens digit must also be greater than 1. Thus, we have the same 6 choices for the tens place: \(2, 3, 4, 5, 6, 7\).

### Step 3: Units place
The units digit must make the number even, meaning the digit has to be one of the even digits. From the set \{0, 1, 2, 3, 4, 5, 6, 7\}, the even digits are \(0, 2, 4, 6\). Thus, there are 4 choices for the units place.

### Total number of even three-digit numbers
To calculate the total number of possible three-digit numbers, we multiply the number of choices for each digit:
\[
6 \times 6 \times 4 = 144
\]

So, there are **144** even three-digit numbers that satisfy the given conditions.

---

Would you like further clarification or any additional details?

### Related Questions:
1. How many odd three-digit numbers can be formed with similar conditions?
2. What if repetition of digits was not allowed? How many numbers would be possible?
3. How many total three-digit numbers (both even and odd) can be formed under the same conditions?
4. What are the possible combinations if only prime digits are allowed for the hundreds and tens places?
5. How many four-digit even numbers can be formed under similar conditions?

### Tip:
When solving problems with digit restrictions, always break the task down step by step, analyzing each digit's constraints individually.

Learn how to form even three-digit numbers using digits 0 to 7 with specific restrictions. The problem covers concepts in combinatorics and counting, emphasizing even numbers and digit constraints. Suitable for Grades 6-8 students, this solution explains the process step by step.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation