1. The problem is to understand how factorial works and see an example. 2. The factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$. 3. The formula is: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 4. Important rules: - $0! = 1$ by definition. - Factorials grow very fast as $n$ increases. 5. Example: Calculate $5!$ $$5! = 5 \times 4 \times 3 \times 2 \times 1$$ 6. Calculate step-by-step: $$5 \times 4 = 20$$ $$20 \times 3 = 60$$ $$60 \times 2 = 120$$ $$120 \times 1 = 120$$ 7. So, $5! = 120$. This means multiplying all integers from 5 down to 1 gives 120.