1. The problem is to understand what factorials are and how to calculate them. 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: - $0!$ is defined as 1. - Factorials grow very fast as $n$ increases. 5. For example, to calculate $5!$: $$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$$ 6. Factorials are used in permutations, combinations, and many areas of mathematics and science.