Question: Joe's iPod has 500 di↵erent songs, consisting of 50 albums of 10 songs each. He listens to 11 random songs on his iPod, with all songs equally likely and chosen independently (so repetitions may occur).
(a) What is the PMF of how many of the 11 songs are from his favorite album?
(b) What is the probability that there are 2 (or more) songs from the same album among the 11 songs he listens to?
(c) A pair of songs is a match if they are from the same album. If, say, the 1st, 3rd, and 7th songs are all from the same album, this counts as 3 matches. Among the 11 songs he listens to, how many matches are there on average?