2 In a survey of university students, 64 had taken mathematics course,
94 had taken computer science course, 58 had taken physics course, 28
had taken mathematics and physics, 26 had taken mathematics and
computer science, 22 had taken computer science and physics course,
and 14 had taken all the three courses. Find the number of students who
were surveyed. Find how many had taken one course only.
Answers
Answer:
Total No.of students surveyed 154
- only maths=24
- only C.S=60
- Only physics=22
only one course studied=24+60+22=106
Step-by-step explanation:
figure in photo
Given:
Let us assume M,C,P to be the sets of students those who had taken mathematics, computer science and physics.
n(M) = 64 students
n(C) = 94 students
n(P) = 58 students
Now the students that had taken two courses together:
n(M∩C) = 26 students
n(M∩P) = 28 students
n(P∩C) = 22 students
n(M∩C∩P) = 14 students
Calculating the number of students who had only taken math:
= n(M) - [n(M∩P) + n(P∩C) - n(M∩C∩P)]
Substituting the values into this formula we get:
= 64 - [28 + 22 - 14]
= 14 students
Therefore, 14 students had only taken math.
Calculating the number of students who had only taken Computer Science:
= n(C) - [n(M∩C) + n(P∩C) - n(M∩C∩P)]
Substituting the values into this formula we get:
= 94 - [26+22-14]
= 60 students
Therefore, 60 students had only taken Computer Science.
Calculating the number of students who only took physics:
= = n(P) - [n(M∩P) + n(P∩C) - n(M∩C∩P)]
= 58 - [28 + 22 - 14]
= 36 students
Therefore, 36 students only took physics.
Calculating the total number of students who had only taken one course:
= 14 + 60 + 36
= 50 students
Therefore, 50 students had only taken one course.
The Total Number of students that were surveyed can be calculated with the help of a Venn Diagram:
= 24 + 12 + 60 + 8 + 14 + 22
= 140 students
Venn Diagram attached below.
