Question

evaluate: 5!

Explanation:

Step1: Recall factorial definition

The factorial of a non - negative integer \(n\), denoted by \(n!\), is the product of all positive integers less than or equal to \(n\). So \(n!=n\times(n - 1)\times\cdots\times1\). For \(n = 5\), we have \(5!=5\times4\times3\times2\times1\).

Step2: Perform the multiplication

\[

$$\begin{align*} 5\times4\times3\times2\times1&=(5\times4)\times3\times2\times1\\ &=20\times3\times2\times1\\ &=(20\times3)\times2\times1\\ &=60\times2\times1\\ &=(60\times2)\times1\\ &=120\times1\\ &=120 \end{align*}$$

\]

Answer:

120