A teacher has 8 students. They pose for a picture by standing in a single line. If the teacher stands on either end of the line, how many different arrangements of the 9 people are possible?

The number of arrangements of the students is:

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8! = 40320

Now the teacher can have only two different positions together with the whole group of students, so 'x 2'

The total combinations will be the product of the number of arrangements of the students and that of the teacher.

Hope it helped! :)