[MATH] PMF Problem

You just rented a large house and your realtor gave you 5 keys, one for each of
the 5 doors of the house. Unfortunately, all keys look identical. Thus, in order to open the front door (one of the 5 doors), you need to try the keys at random. Find the pmf of the number of trials you will need to open the front door, in each of the following cases:
(a) After an unsuccessful trial, you mark the corresponding key so that you don’t try it again;
(b) At each trial, you are equally likely to choose any key.