We are given the equation:

\[
\frac{(n-4)!}{(n-5)!} = 15
\]

### Step-by-step solution:

1. Recall that \(\frac{(n-4)!}{(n-5)!}\) simplifies as follows:
   \[
   \frac{(n-4)!}{(n-5)!} = (n-4)
   \]
   This is because \((n-4)! = (n-4) \cdot (n-5)!\), and dividing by \((n-5)!\) leaves just \((n-4)\).

2. Therefore, the equation becomes:
   \[
   (n-4) = 15
   \]

3. Solve for \(n\):
   \[
   n - 4 = 15
   \]
   \[
   n = 19
   \]

Thus, the solution is \(n = 19\).

Would you like further details or have any questions?

Here are 5 questions to deepen understanding:
1. What happens if we change the factorial argument in the equation?
2. How do factorial properties simplify division like in this problem?
3. Can you solve the problem for different values of \(15\)?
4. How can you graph this kind of equation?
5. What real-world scenarios can factorials like these model?

**Tip:** Always remember that \(\frac{a!}{(a-k)!} = a(a-1)(a-2)\dots(a-k+1)\), which simplifies many factorial expressions.

Learn how to solve the factorial equation \frac{(n-4)!}{(n-5)!} = 15 with a detailed step-by-step solution. This problem involves simplifying factorial expressions and basic algebra. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation