Factorial (\(n!\) notation)

The factorial of a non-negative integer \(n\), written \(n!\) (“\(n\) factorial”), is the product of all positive integers from \(n\) down to \(1\).
\(n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1\)

Examples
\(3! = 3 \times 2 \times 1 = 6\)
\(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)

By definition, \(0! = 1\). Factorials are often used to count arrangements. For example, \(3\) different books can be arranged in \(3! = 6\) different orders.