# How many ways can 30 students be arranged in a 4- student line?

Apr 20, 2016

$657 , 720$ ways

#### Explanation:

I have assumed that what is meant is:
"How may ways can a group of 4 students be extracted from a group of 30 students, when the order of extraction is significant?"

In this case:
$\textcolor{w h i t e}{\text{XXX}}$There are $30$ candidates for the first selection
$\textcolor{w h i t e}{\text{XXX}}$For each of the first selections there are $29$ candidates for the second selection
$\textcolor{w h i t e}{\text{XXX}}$For each of these first and second selections there are $28$ candidates for the third selection.
$\textcolor{w h i t e}{\text{XXX}}$For each of these first, second, and third selections there are $27$ candidates for the fourth selection.

Therefore there are
$\textcolor{w h i t e}{\text{XXX}} 30 \times 29 \times 28 \times 27 = 657 , 720$ possible selections.