There are n students in your probability class. At the beginning of the exam, each student labels and drops off their phone in a box at the front of the room. The professor is absent-minded, though, and loses track of all the labels. So at the end of the exam he gives everybody a random phone from the box. Each allocation of phones to students is equally likely.

(i) How many possible allocations are there?

(ii) What is the probability that you get your own phone back?

(iii) You typically study with a group of 3 students (including yourself). What is the probability that you or one of your two study partners gets your phone?

(iv) Half of the phones are iPhones, and the other half are androids. (Assume n is even.) What is the probability that every iPhone user gets an android, and vice versa?