In a school of 120 students it was found out that 75 read English, 55 read science and 35 read biology. All the 120 students read at least one of three subject and 49 read exactly two subjects. How many students read all the three subjects?
I have spent all day but I couldn't solve it help me please!
$\endgroup$ 41 Answer
$\begingroup$By the Principle of Inclusion Exclusion, we must add up the number of students reading English, the number of students reading Science, and the number of students reading Biology. Then we must subtract this sum from the number of people reading English and Science, the number of people reading Science and Biology, and the number of students reading Biology and English. Finally, we must add back the number of students reading all three of the subjects; this calculates the number of students in the school. Let $x$ be the number of students reading all three of the subjects. We now have the equation
$75+55+35-49+x=120$
Solving for $x$ yields $\boxed{4}$ as the number of students reading all three of the subjects.
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