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I see that you've uploaded an image containing mathematical problems, likely related to probability and combinatorics. I'll extract the questions and help solve them. Here's a summary of the questions:

1. **Books in a library**: 
   - There are 3 mathematics books and 5 physics books in a library. How many ways can you select one book from the library?

2. **Key combination**: 
   - To unlock a key, you need to choose 1 digit from the first 4 digits and 1 digit from the last 6 digits. How many combinations are possible?

3. **Factorial problem**: 
   - If \( n! = 120 \), find the value of \( n \).

4. **Factorial division**:
   - Compute \( \frac{8!}{(8-3)!} \).

5. **Rearranging letters**: 
   - How many ways are there to arrange the first 3 letters of the word "MAKAN"?

6. **Choosing books**: 
   - How many ways are there to select 4 books out of 6 different books?

7. **Class selection**: 
   - From a class of 12 students, how many ways can 3 students be chosen to become class officers?

8. **Word "MATEMATIKA"**: 
   - How many ways can you rearrange 2 letters from the word "MATEMATIKA"?

9. **Red and blue balls**: 
   - A bag contains 3 red balls and 5 blue balls. If one ball is drawn at random, what is the probability of drawing a red ball?

10. **Cards**: 
    - From a deck of 52 cards, what is the probability of drawing an Ace?

11. **Lottery ticket**: 
    - If 100 tickets are sold and 3 winners are chosen, what is the probability that a person who buys 2 tickets wins at least one prize?

12. **Balls with specific conditions**: 
    - A bag contains 6 red balls and 6 white balls. Two balls are randomly drawn without replacement. What is the probability that the first ball is red and the second ball is white?

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Let me start by solving the first few problems.

1. **Choosing a book**:  
   Total books = 3 mathematics + 5 physics = 8.  
   The number of ways to select 1 book is simply 8.

2. **Key combination**:  
   You need to choose 1 digit from the first 4 digits and 1 from the last 6 digits.  
   The total combinations = \( 4 \times 6 = 24 \).

3. **Factorial problem**:  
   \( n! = 120 \). We know \( 5! = 120 \), so \( n = 5 \).

4. **Factorial division**:  
   \( \frac{8!}{(8-3)!} = \frac{8!}{5!} \).

I'll continue to solve the remaining problems. Let me know if you want a specific problem explained in more detail! Here are five related questions for practice:

1. How would the calculation change if there were 10 books in total with different proportions of math and physics books?
2. How do you compute combinations for more complex key lock combinations with multiple digits?
3. What is the factorial of 6, and how can it be applied in a similar problem?
4. How many ways are there to arrange 4 letters from the word "COMPUTER"?
5. If you select 2 students from a group of 10, how many possible pairs can you form?

**Tip**: Remember, combinations are used when order doesn't matter, while permutations are used when the order is important.

There are multiple math problems related to probability and combinatorics, including selecting books, unlocking a key combination, calculating factorials, arranging letters, selecting students, probability with balls, and drawing cards.

Solve various problems on probability and combinatorics. Topics include selecting books, unlocking key combinations, calculating factorials, arranging letters, selecting students, and probability with balls and cards. Suitable for high school students in Grades 10-12.

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