There are 12,650 ways a teacher can group 4 students in a class that has 25 students.

This is a combination problem, and the formula for the number of ways to choose r items from a set of n items is nCr = n!/r!(n-r)!. In this case, we want to choose 4 students from a set of 25, so the number of ways to group them is 25C4 = 25!/4!21! = 12,650.