The expression given in the image is:

$\frac{2! \times 5!}{6 \times 3!}$

To simplify this expression:

1. Start by calculating the factorials:

   • $2! = 2 \times 1 = 2$
   • $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$
   • $3! = 3 \times 2 \times 1 = 6$

2. Substitute these values back into the expression:

$\frac{2 \times 120}{6 \times 6}$

3. Simplify the expression:
   • The denominator is $6 \times 6 = 36$
   • The numerator is $2 \times 120 = 240$

So, the expression becomes:

$\frac{240}{36}$

4. Simplify the fraction by dividing both the numerator and denominator by 12:

$\frac{240 \div 12}{36 \div 12} = \frac{20}{3}$

Thus, the simplified result is:

$\frac{20}{3}$

Would you like further clarification on any step? Here are some related questions:

1. How do you calculate a factorial for larger numbers?
2. What is the general method to simplify fractions?
3. How can factorials be applied in probability problems?
4. What happens if we change the values of the numbers in the factorial expressions?
5. How does this method relate to combinatorics?

Tip: When simplifying factorial expressions, try to cancel out terms from the numerator and denominator early to make the calculations easier!