in a school servey64 students have taken math 94 chemistry 58 physics 28 math & physics 26 math & chemistry 22 chemistry & physics 14 had taken all courses find how many had taken 1 course only by venn digram
Answers
Hey guys!!!!
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CALCULATEING THE TOTAL NO. OF STUDENTS WHO HAD ONLY TAKEN ONE COURSE
=> n(m) + n(c) + n(p)
=> 14+60+36
=>50
Therefore, 50 students had only taken one course.
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Answer:
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.
