56. An event independently occurs on each day with probability p. Let denote the total number of events that occur on the first n days, and let denote the day on which the rth event occurs.

(a) What is the distribution of ?

(b) What is the distribution of Image?

(c) What is the distribution of ?

(d) Given that , show that the set of r days on which events occurred has the same distribution as a random selection (without replacement) of r of the values .