The text is in Korean, and from what I can analyze, it appears to be a mathematical or combinatorial question related to the digits or numbers 3, 4, and 5. Please allow me to transcribe and interpret it for solving.Here is the transcribed question from the image:

• The digits used in the number 345 are 3, 4, and 5.
• How many three-digit numbers can be formed if exactly two of the digits used in the number are identical, and the third digit is one of the other digits (from 3, 4, or 5)?

Let's analyze and solve the problem systematically.

Step 1: Conditions

The number must:

1. Be three digits long.
2. Contain two identical digits and one different digit.
3. Only use the digits 3, 4, and 5.

Step 2: Breakdown of Solutions

• Select the digit to be repeated. There are 3 choices (3, 4, or 5).
• Select the third digit, which must be different from the repeated digit. There are 2 choices for this.
• Arrange these digits into a three-digit number. The arrangements are calculated using permutations of the set with repetition. For a set like {x, x, y}, the total number of permutations is:

$\text{Number of arrangements} = \frac{3!}{2!} = 3$

Thus, for each choice of the repeated digit and the third digit: $\text{Total numbers} = 3 \times 2 = 6$

Step 3: Total Numbers

Since there are 3 options for the repeated digit, and for each, there are 6 possible numbers: $\text{Total numbers} = 3 \times 6 = 18$

Final Answer:

18 numbers can be formed following the given conditions.

Would you like a detailed explanation of permutations, or do you have additional questions?

Related Questions:

1. How would the solution change if the digits were not restricted to 3, 4, and 5?
2. How can this problem be solved using a different method, such as combinations and cases?
3. What if all three digits were required to be distinct?
4. What if the problem specified no digit could be repeated more than once?
5. Can we generalize this method to find similar patterns with larger sets of digits?

Tip:

When working with permutations and combinations, always clarify whether repetition is allowed or restricted to avoid errors in your calculations!