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500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects? Correct Answer 53

n(C) = 329

n(P) = 186

n(M) = 295

n(C⋂P) = 83

n(C⋂M) = 217

n(P⋂M) = 63

n(P⋃C⋃M) = 500

n(P⋃C⋃M) = n(P) + n(C) + n(M) - n(P⋂C) -n (C⋂M) - n(M⋂C) + n(P⋂C⋂M)

500 = 186 + 329 + 295 - 83 - 217 - 63 + n(P⋂C⋂M)

n(P⋂C⋂M) = 53

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