In a group of 80 students, 40 study Music, 35 study Dance and 30 study Drama. Also 15 study Music and Dance, 12 study Dance and Drama, 10 study Music and Drama, and 5 study all three. How many students study exactly two of the three subjects?

Each pairwise count includes the 5 students who study all three, so those 5 must be removed once from each pair: (15 − 5) + (12 − 5) + (10 − 5) = 10 + 7 + 5 = 22 students. Adding the pairwise counts as they stand gives 37, subtracting the 5 only once gives 32, and 27 is 22 plus the all-three group, which the phrase 'exactly two' excludes.