### Instruction: In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-two students are registered for Math, and thirty-five students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
Answer Choices: (A) 13 (B) 10 (C) 9 (D) 8 (E) 7.### Response: A U B U C = A + B + C - AB-BC-AC + ABC
68 = 25 + 22+ 35 -AB-BC-AC +3 => AB+BC+AC = 17
Exactly Two classes = AB+BC+AC - 3ABC = 17 -3*3 = 8
Hence D