https://file.aiquickdraw.com/mathbot/file/1726622894829lcq94w6g.jpg

The image shows the following expression to compute:

\[
\frac{n!}{(n - 3)!}
\]

### Solution:
The factorial function \(n!\) is defined as the product of all positive integers from 1 to \(n\). When we divide two factorials, such as \(\frac{n!}{(n - 3)!}\), we can cancel terms to simplify.

1. Start by expanding \(n!\):
   \[
   n! = n \cdot (n-1) \cdot (n-2) \cdot (n-3)!
   \]
   
2. The \( (n - 3)! \) in the denominator will cancel out the \( (n - 3)! \) in the numerator, leaving:
   \[
   \frac{n!}{(n - 3)!} = n \cdot (n-1) \cdot (n-2)
   \]

Thus, the simplified result is:

\[
n \cdot (n-1) \cdot (n-2)
\]

Would you like a more detailed explanation, or have any questions about this? 

### Related Questions:
1. How is the factorial function defined for non-integer values?
2. How would you compute \(\frac{n!}{(n - k)!}\) for any \(k\)?
3. What is the binomial coefficient and how does it relate to factorials?
4. Can you express \(n!\) in terms of the Gamma function?
5. How would you apply this formula if \(n = 6\)?

### Tip:
When simplifying factorials, look for common terms in the numerator and denominator to make cancellations easier.

Learn how to simplify the expression n! / (n - 3)! using factorial rules and algebraic simplification. Suitable for high school students in Grades 10-12.

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