The equation shown in the image is:

$\frac{15!}{13! \times 3!}$

To simplify this expression, let's break it down step by step:

1. Factorial Definition:

   • $15! = 15 \times 14 \times 13 \times 12 \times \dots \times 1$
   • $13! = 13 \times 12 \times 11 \times \dots \times 1$
   • $3! = 3 \times 2 \times 1 = 6$

2. Simplify Factorials:

   • We can cancel out the common $13!$ in both the numerator and denominator:

   $\frac{15!}{13! \times 3!} = \frac{15 \times 14 \times 13!}{13! \times 3!}$

   The $13!$ terms cancel out, leaving us with:

   $\frac{15 \times 14}{3!} = \frac{15 \times 14}{6}$

3. Simplify Further:

   • Multiply 15 and 14: $15 \times 14 = 210$
   • Divide by 6: $\frac{210}{6} = 35$

So, the final result is:

$\boxed{35}$

Would you like further details on factorials or another related topic?

Here are some related questions you might find interesting:

1. How do we define a factorial in mathematics?
2. What are some properties of factorials that can simplify complex calculations?
3. How do combinations and permutations relate to factorials?
4. What is the difference between $n!$ and $(n-1)!$?
5. Can factorials be computed efficiently for very large numbers?

Tip: Factorial operations can be simplified by canceling out common terms in the numerator and denominator to avoid calculating large numbers.