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Question

A class has ,175 students. the following table shows the number of students studying one or more of the following subjects in this class. find how many students are enrolled in mathematics alone, physics alone, and chemistry alone? are there students who have not been offered any of these three subjects?

SubjectNumber of students
Mathematics100
Physics70
Chemistry46
Mathematics and Physics30
Mathematics and Chemistry28
Physics and Chemistry23
Mathematics, Physics and Chemistry18

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Solution

Step 1.Find the number of students who studied maths or physics or chemistry

From the given table,

Total number of students, n(U)=175

Total number of students enrolled in Mathematics alone, n(M)=100

Total number of students enrolled in Physics alone, n(P)=70

Total number of students enrolled in Chemistry alone, n(C)=46

So that, n(U)=175,n(M)=100,n(P)=70andn(C)=46

n(MP)=30,n(MC)=28,n(PC)=23,andn(MPC)=18

The number of students who studied maths or physics or chemistry is given by n(MPC) .

n(MPC)=n(M)+n(P)+n(C)-n(MP)-n(MC)-n(PC)+n(MPC)=100+70+46-30-28-23+18=234-81=153

Step 2. Calculate the total number of students enrolled in Mathematics alone.

The number of students enrolled in Mathematics alone is computed as,

Numberofstudents=n(M)-n(MP)-n(MC)+n(MPC)=100-30-28+18=118-58=60

Thus, the total 60 students enrolled in Mathematics alone.

Step 3. Calculate the total number of students enrolled in Physics alone.

The number of students enrolled in physics alone is computed as,

Numberofstudents=n(P)-n(MP)-n(PC)+n(MPC)=70-30-23+18=88-53=35

Thus, the total 35 students enrolled in physics alone.

Step 4. Calculate the total number of students enrolled in Chemistry alone.

The number of students enrolled in Chemistry alone is computed as,

Numberofstudents=n(C)-n(MC)-n(PC)+n(MPC)=46-28-23+18=64-51=13

Thus, the total 13 students enrolled in chemistry alone.

Step 5. Calculate the number of students who have not been offered any of these three subjects.

The number of students who have not been offered any of these three subjects is computed as,

Numberofstudents=175-153=22

Thus, there are 22 students who have not been offered any of these three subjects.

Hence,

The total 60 students enrolled in Mathematics alone.

The total 35 students enrolled in physics alone.

The total 13 students enrolled in chemistry alone.

There are 22 students who have not been offered any of these three subjects.


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