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The image shows a series of factorial problems, asking to calculate the values of specific factorials. Let’s work through these one by one, presenting the calculations:

1) \(0! \)
- By definition: \( 0! = 1 \).

2) \( 1! \)
- Similarly: \( 1! = 1 \).

3) \( 6! \)
- \( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \).

4) \( 7! \)
- \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \).

5) \( (2! + 3!) \)
- \( 2! = 2 \times 1 = 2 \), and \( 3! = 3 \times 2 \times 1 = 6 \),
- So, \( 2! + 3! = 2 + 6 = 8 \).

6) \( (1! + 4!) \)
- \( 1! = 1 \), and \( 4! = 4 \times 3 \times 2 \times 1 = 24 \),
- So, \( 1! + 4! = 1 + 24 = 25 \).

7) \( 3! - 2! \)
- \( 3! = 6 \), and \( 2! = 2 \),
- So, \( 3! - 2! = 6 - 2 = 4 \).

8) \( (0! + 1!) \)
- \( 0! = 1 \), and \( 1! = 1 \),
- So, \( 0! + 1! = 1 + 1 = 2 \).

9) \( 2! \times 3! \)
- \( 2! = 2 \), and \( 3! = 6 \),
- So, \( 2! \times 3! = 2 \times 6 = 12 \).

10) \( 0! \times 5! \)
- \( 0! = 1 \), and \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \),
- So, \( 0! \times 5! = 1 \times 120 = 120 \).

Would you like more detailed explanations or have any further questions?

### Related Questions:
1. What is the definition of factorial and how does it work?
2. How does the value of factorial grow as the number increases?
3. Can factorial operations be extended to non-integer numbers?
4. What is the relationship between factorials and permutations?
5. What is Stirling's approximation and how does it apply to large factorials?

**Tip:** Factorials grow very quickly, making them useful in combinatorics and probability theory.

Learn how to calculate factorial values for expressions like 0!, 1!, 6!, 7!, and others. This problem involves the factorial definition and arithmetic operations. Suitable for students in Grades 7-9.

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