Question

In a survey of university students, 64 had taken java course, 94 had taken C++ course, 58 had taken PhP course, 28 had taken java and PhP, 26 had taken java and C++, 22 had taken C++ and PhP course, and 14 had taken all the three courses. Find how many had taken one course only

Answer 1

106 students had taken only one course

Step-by-step explanation:

Java Courses  J = 64

C ++ Courses C= 94

Php Courses P = 58

java and PhP  J ∩ P = 28

Jjava and C++, J ∩ C = 26

C++ and PhP  C ∩ P = 22

all three J ∩ P ∩ C  = 14

Only Java  = J  - J ∩ P - J ∩ C + J ∩ P ∩ C

= 64 - 28 - 26 + 14

= 24

Only C ++   =C  - C ∩ P - J ∩ C + J ∩ P ∩ C

= 94 - 22 - 26 + 14

= 60

Only PHP = P  - C ∩ P - J ∩ P + J ∩ P ∩ C

= 58 - 22 - 28 + 14

= 22

only one course = 24 + 60 + 22

= 106

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Answer 2

No. of students who do one course only are 106 students

•By analysing the situation carefully venn diagram is drawn to solve the problem further.

•Now,

•64 had taken java course

n(j) = 64

•94 had taken C++ course

n( C++) = 94

•58 had taken PhP course

n(p) = 58

•28 had taken java and PhP

n(j intersection p ) = 28

•26 had taken java and C++

n( C++ intersection p) = 26

•22 had taken C++ and PhP course

n(C++ intersection p) = 22

•14 had taken all the three courses

n (j intersection C++ intersection p)

= 14

•n(j intersection p ) only = 28 -14 = 14

•n( C++ intersection p) only = 26 -14 = 12

•n(C++ intersection p) only = 22 - 14 = 8

•n(j) only = 64 - 22 - 14 - 14 = 24

•n( C++) only = 94 -12 - 14 - 8 = 60

•n(p) only = 58 -14 - 14 - 8 = 22

•No. of students who do one course only = 24 + 22 + 50 = 106 students