there are 4 students sitting on the stage at the school assembly waiting to receive their prizes.Alan and Julia wanted to sit together. If they did,how many different arrangements of students would there be?

Answer 1

consider Alan and Julia as one person.

So, there are really only 3 students, making 3! = 6 arrangements.

However, Alan and Julia may switch places, so there are 12 total arrangements.

Answer 2

Sitting in the school cafeteria you notice the different groups of students sitting together. Which group would you think might be characterized as a clique?