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# Mathematics

in a class of 80 students,40 study physics, 48 study mathematics and 4 4 study chemistry. 20 study physics and mathematics. 24 study physics and chemistry and 32 study only two of the three subjects. if every student studies at least one of the three subjects, find
1 . the number of students who study all the three subjects.
2 . the number of students who study only mathematics and chemistry?

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1. I need solution for the question.

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2. If you are studying this topic , you must have learned about Venn diagrams.

Draw 3 overlapping circles.
label the intersection of all 3 as x
low look at the double courses
e.g. 20 study physics and math. That would be the intersection of
the physics and the math circles, which already contains an x
So label the part of physics and math but not chemistry as 20-x

continue likewise for the rest of the data.
You should have all the regions filled in.

Answers can now be written by simply looking at these regions.

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3. use calculator much faster than using this forum
unless you're trying to figure out how to do somehting

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