SOLUTION: There are a group of 48 students enrolled in mathematics, french and physics. Some students were more successful then others: 32 passed French, 27 passed physics, 33 passed mathem

Question 1177380: There are a group of 48 students enrolled in mathematics, french and physics. Some students were more successful then others: 32 passed French, 27 passed physics, 33 passed mathematics; 26 passed French and math, 26 passed physics and math, 21 passed french and physics, and 21 passed French, math and physics.
How many students passed one or more of the subjects? Solve the question using the inclusion-exclusion principle. Show your calculations.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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There IS a group of 48 students enrolled in Mathematics, French and Physics.
Some students were more successful THAN others: 32 passed French, 27 passed Physics, 33 passed Mathematics;
26 passed French and Math, 26 passed Physics and Math, 21 passed French and Physics, and 21 passed French, Math and Physics.
How many students passed one or more of the subjects? Solve the PROBLEM using the inclusion-exclusion principle.
Show your calculations.
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So, you want to find the number of students in the union set  

    (passed French) U (passed Physics) U (passed Math)


or, in simple terms, you want to determine the number of students who passed at least one subject.



Apply the inclusion-exclusion principle


    n(F U P U M) = n(F) + n(P) + n(M) - n(F ∩ P) - n(F ∩ M) - n(P ∩ M) + n(F ∩ P ∩ M)

        (alternate sum)



Now substitute all given numbers and obtain the ANSWER


    n(F U P U M) = 32 + 27 + 33 - 26 - 26 - 21 + 21 = 40.


ANSWER.  The number of those who passed at least one subject is/was 40.

Solved.

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