Answer
$5040$ different ways.
Work Step by Step
They have to select 4 of 10 seats. The order that the seats are chosen is important. That is, if student 1 selects seat 4 and student 2 select seat 8, it is different from student 1 selecting seat 8 and student 2 selecting seat 4.
Permutation of 10 distinct seats taken 4 at a time:
$_{10}P_4=\frac{10!}{(10-4)!}=\frac{10!}{6!}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{6\times5\times4\times3\times2\times1}=10\times9\times8\times7=5040$
