A school has four art teachers, three music teachers, and eight history teachers. In how many ways can a student be assigned an art teacher, a music teacher, and a history teacher?

There are 4 art teachers, 3 music teachers, 8 history teachers. So, there are 4 ways to select an art teacher, 3 ways to select a music teacher and 8 ways to select a history teacher to assign the student.

According to the fundamental principal of counting, the total number of ways to assign a student to these teachers will be the product of the ways of assigning the student to each subject.

So, the number of a student can be assigned an art teacher, a music teacher, and a history teacher = 4 x 3 x 8 = 96 ways.