https://file.aiquickdraw.com/mathbot/file/1727406511901aavpzpqa.jpg

The expression to evaluate from your image is:

\[
\frac{5!}{3!(5 - 3)!}
\]

Let's break this down:

1. \( 5! \) means \( 5 \times 4 \times 3 \times 2 \times 1 = 120 \).
2. \( 3! \) means \( 3 \times 2 \times 1 = 6 \).
3. \( (5 - 3)! = 2! \), which is \( 2 \times 1 = 2 \).

Now, substitute these into the expression:

\[
\frac{5!}{3! \times (5 - 3)!} = \frac{120}{6 \times 2} = \frac{120}{12} = 10
\]

So, the answer is \( 10 \).

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How do factorials work and why are they useful in combinatorics?
2. What is the significance of permutations in mathematics?
3. Can you explain how the binomial coefficient is related to factorials?
4. How does simplifying expressions involving factorials work?
5. In what real-world situations might factorials and combinations be used?

**Tip:** When simplifying expressions involving factorials, always look for common terms that can be canceled out to make the computation easier.

Evaluate the expression 5! / [3!(5 - 3)!] without using a calculator.

Learn how to simplify the factorial expression 5! / [3!(5 - 3)!] step by step without using a calculator. This problem demonstrates core concepts in combinatorics and simplification techniques suitable for students in Grades 9-12.

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