Question: Each of 111 people names his or her 5 favorite movies out of a list of 11 movies.
(a) Alice and Bob are 2 of the 111 people. Assume for this part only that Alice's 5 favorite movies out of the 11 are random, with all sets of 5 equally likely, and likewise for Bob, independently. Find the expected number of movies in common to Alice's and Bob's lists of favorite movies.
(b) Show that there are 2 movies such that at least 21 of the people name both of these movies as favorites.