1. The problem is to understand and compute the factorial of a number $n$, denoted as $n!$. 2. The factorial of a non-negative integer $n$ is the product of all positive integers less than or equal to $n$. The formula is: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 3. Important rules: - By definition, $0! = 1$. - Factorials grow very quickly as $n$ increases. 4. For example, if $n=5$, then: $$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$$ 5. Factorials are used in permutations, combinations, and many areas of mathematics and science. 6. To compute $n!$, multiply all integers from 1 up to $n$ inclusively. Final answer: $n! = n \times (n-1) \times \cdots \times 1$