Find the number of ways in which six teachers can be assigned to four sections of introductory mathematics if no teacher must be assigned to more than one section?

So 4 sections
6 options for first section
5 options for second (since one was used for first)
4 options
3 options
mutiply
6 times 5 times 4 times 3=360

answer is 360 ways

The first section can be taught by any one of
the 6 teachers.                               For each one . . .
The 2nd section can be taught by any one of
the remaining 5 teachers.              For each one . . .
The 3rd section can be taught by any one of
the remaining 4 teachers.              For each one . . .
The 4th section can be taught by any one of
the remaining 3 teachers.

So the number of possible teams of teachers for all four
math sections is
                
                   (6 x 5 x 4 x 3)  =  360 different teams.

Notice that whichever team is selected, there will be two teachers
who have no class to teach during the introductory math hour.

This makes absolutely no sense at all young man/women