Question

How many ways can 9 students be seated in a row if 3 must be sat together?

Answer 1

start by treating the 3 students as 1 since they have to sit together.
9 people (A,B,C,D,E,F,G,H,J) becomes ( X,D,E,F,G,H,J) where the X is the 3 students.

so how many ways you can arrange 9-2 = 7 students?
7! = 5040

then consider that the 3 students that must sit together can have 6 different arrangements. 3! = 6 ; (abc, acb, bca, bac, cab, cba)

answer = 7! 3!
5040*6 = 30,240 ways