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Question

In a class 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of those 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students are offered all the three subjects, find the total number of students.


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Solution

Find the total number of students.

Assume that, P denotes Physics, C denotes Chemistry, M denotes Mathematics and n denotes the number of students.

So, nCM denotes the number of students who took both Chemistry and Mathematics.

nPC denotes the number of students who took both Physics and Chemistry.

nPM denotes the number of students who took both Physics and Mathematics.

nPCM denotes the number of students who took all the three subjects.

And nPCM denotes the total number of students in the class.

So, the given data can be represented as follows:

n(P)=18n(C)=23n(M)=24n(CM)=13n(PC)=12n(PM)=11n(PCM)=6

Since, the formula of n(ABC)=n(A)+n(B)+n(C)-n(AB)-n(BC)-n(AC)+n(ABC).

The total number of students n(PCM) can be given as:

n(PCM)=18+23+24-13-12-11+6n(PCM)=35

Therefore, the total number of students is 35.


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