This equation involves factorials and can be simplified using properties of factorials. The given equation is:

$\frac{17!}{15! \cdot 3!}$

Let's break it down:

1. Factorial Expansion: Factorials expand as products of integers. We know:

   • $17! = 17 \times 16 \times 15!$
   • So, $\frac{17!}{15!} = 17 \times 16$.

2. Simplifying the Expression: Now, we have: $\frac{17!}{15! \cdot 3!} = \frac{17 \times 16 \times 15!}{15! \cdot 3!}$ The $15!$ terms cancel out, leaving: $\frac{17 \times 16}{3!}$

3. Calculate $3!$: $3! = 3 \times 2 \times 1 = 6$

4. Final Calculation: $\frac{17 \times 16}{6} = \frac{272}{6} = 45.33$

Therefore, the simplified value of the expression is approximately 45.33.

Would you like further details or have any questions about this?

Here are some related questions for you:

1. What is the general rule for simplifying factorial expressions?
2. How would you approach a factorial expression involving larger numbers?
3. Can factorials be used in combinatorics, and if so, how?
4. How do you calculate large factorials efficiently?
5. What are some common properties of factorials?

Tip: Always try to cancel out common terms in factorial expressions to simplify them before performing the multiplication.