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.