https://file.aiquickdraw.com/mathbot/file/1727299154931kekkpft0.jpg

The image contains a problem written in Indonesian, which roughly translates to:

"Given the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9, how many different four-digit numbers can be formed from these digits, where each number is composed of exactly four digits?"

### Problem Explanation:
You are asked to form a four-digit number using the digits 1 through 9, and the task is to determine how many such numbers can be created.

### Assumptions:
- No specific rules are mentioned regarding repetition or order. Let's consider two cases:
  1. **Repetition of digits is allowed**: You can use any digit multiple times.
  2. **Repetition of digits is not allowed**: Each digit can be used only once.

### Case 1: Repetition of digits is allowed
Since there are 9 digits available (1-9), and you are selecting 4 digits where repetition is allowed, the number of possibilities for each of the 4 positions in the number is 9.

So, the total number of four-digit numbers is:

\[
9 \times 9 \times 9 \times 9 = 9^4 = 6561
\]

### Case 2: Repetition of digits is not allowed
If repetition is not allowed, for the first digit, you have 9 choices. For the second digit, you will have 8 remaining choices, for the third, 7 choices, and for the fourth digit, 6 choices.

So, the total number of four-digit numbers is:

\[
9 \times 8 \times 7 \times 6 = 3024
\]

### Conclusion:
- If repetition **is allowed**, the number of different four-digit numbers is **6561**.
- If repetition **is not allowed**, the number of different four-digit numbers is **3024**.

Would you like further clarification on any part? Let me know if you want more details!

---

Here are 5 questions that expand on this concept:

1. How would the solution change if the digits 0 through 9 were used instead?
2. What happens if we are asked to form five-digit numbers instead of four-digit numbers?
3. How can we approach the problem if the number must be divisible by a certain digit, say 5?
4. What if we are only allowed to use even digits to form the number?
5. How many four-digit palindromic numbers can be formed from these digits?

**Tip**: Always carefully check the problem's constraints, especially regarding repetition, to ensure you are applying the correct formula.

Given the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9, how many different four-digit numbers can be formed from these digits, where each number is composed of exactly four digits?

Learn how to calculate the number of different four-digit numbers that can be formed using the digits 1 to 9. This problem explores key combinatorial concepts such as permutations and the fundamental principle of counting. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation