Inclusion-Exclusion and The Movies
Who doesn’t love a great movie? James Franco, Jonah Hill, and Seth Rogen have been in some funny movies, but how many movies are there that any one of these actors are in? Our first guess might be to add all the movies all three of them have been in. But that will not only include movies that one of the actors was in, it will also include movies that starred two or three of them. For this problem, we will need to use the principle of inclusion-exclusion.
Let’s first review the rule of sum: “The rule of sum states that if an action is performed by making A choices or B other choices, then it can be performed A + B ways.” (Benjamin, 8)
So the reason we cannot simply add the list of movies for each of these actors is because we know that they share some of the same movies. The two lists must be distinct in order for us to directly add them.
Take a look at the picture below: