Question

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

Answer 1

`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:
`color(white)("XXX")`There are `30` candidates for the first selection
`color(white)("XXX")`For each of the first selections there are `29` candidates for the second selection
`color(white)("XXX")`For each of these first and second selections there are `28` candidates for the third selection.
`color(white)("XXX")`For each of these first, second, and third selections there are `27` candidates for the fourth selection.

Therefore there are
`color(white)("XXX")30xx29xx28xx27=657,720` possible selections.