User:Julia Hartman

Girl's Night
Audrey, Brooke and Caroline are planning a long movie night. They want to binge-watch some films together from their favorite director. But they can't decide on the selection of movies, because they have a deal that they must all agree on the films they watch. Moreover, their preferences are very different, and there are eleven titles to choose from. After long discussions, Caroline proposes the following: "Each one of us independently writes a list of five of the eleven titles. The order is not important." Audrey is enthusiastic about the idea. Brooke, on the other hand, is skeptical, saying, "I don't think we can agree on more than two titles using this procedure."

What is the probability that more than two of the same titles are found on all three lists?