A company of n students decides to have lunch at the Student Union on a particular day. Each of the students will go alone as they attend different classes in the morning. However, there are k restaurants at the Student Union and they have not specified at which one they are supposed to meet.

(i) How many different selections are possible for the restaurants that the students will go for lunch?

(ii) Assuming that each student chooses a restaurant at random with the same probability, what is the probability that they all choose the same restaurant?