# Inclusion exclusion principle counting

50 students traveled to Europe, last year. Of these, 12 visited Amsterdam, 13 went to Berlin, and 15 were in Copenhagen. Some visited two cities: 3 visited both Amsterdam and Berlin, 6 visited Amsterdam and Copenhagen, and 5 visited Berlin and Copenhagen. But only 2 visited all three cities.

Question : How many students visited Copenhagen, but neither Amsterdam nor Berlin?

I have done the graph and I think the answer is 6 but I would like to learn how to compute it.

Thank you!

Let $$|A|$$, $$|B|$$, and $$|C|$$ denote, respectively, the number of students who visited Amsterdam, Berlin, and Copenhagen.
$$|C| - |A \cap C| - |B \cap C| + |A \cap B \cap C| = 15 - 6 - 5 + 2 = 6$$ as you found.