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Failing Class


An examination in three subjects, Algebra, Biology, and Chemistry was taken by 41 students. The following table shows how many students failed in each single subject and in their various combinations:

Subject: A B C AB AC BC ABC

Failed: 12 5 8 2 6 3 1

For instance, 5 students failed in Biology, among whom there were 3 failing both in Biology and in Chemistry, and just one of these 3 failed in all three subjects.

How many students passed in all three subjects?

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