Question

In how many ways can a teacher arrange 6 students in the front row if there are 30 total students?

Answer 1

Assuming order doesn't matter:
30c6 = 593,775

Answer 2

The use of the word "arrange" in the question indicates that the order does matter. If the order was not important the word "select" would probably been used.
Therefore the number of permutations of the 30 students taken 6 at a time is:
\[30P6=\frac{30!}{(30-6)!}=427,518,000\]