In how many ways can 6 people be lined up to get on a bus?

Jan 27, 2016

6! = 720

Explanation:

$6$ choices for the first person;
$\textcolor{w h i t e}{\text{XX}}$for each of these, $5$ choices for the next;
$\textcolor{w h i t e}{\text{XXXX}}$for each of these, $4$ choices for the next;
$\textcolor{w h i t e}{\text{XXXXXX}}$for each of these, $3$ choices for the next;
$\textcolor{w h i t e}{\text{XXXXXXXX}}$for each of these, $2$ choices for the next;
$\textcolor{w h i t e}{\text{XXXXXXXXXX}}$for each of these, $1$ choice for the last person.

6xx5xx4xx3xx2xx1 = 6! = 720