There are 2504 computer science students at a school. Of these, 1876 have taken a course in Java, 999 have taken a course in Linux, and 345 have taken a course in C. Further, 876 have taken courses in both Java and Linux, 231 have taken courses in both Linux and C, and 290 have taken courses in both Java and C. If 189 of these students have taken courses in Linux, Java, and C, how many of these 2504 students have not taken a course in any of these three subjects?

492

Step-by-step explanation:

As per the given data of the question:

Total number of students = 2504

Number of students in Java (J) = 1876

Number of students in Linux (L) = 999

Number of students in C = 345

J∩L = 876

L∩C = 231

C∩J = 290

L∩J∩C = 189

Now according to Venn-diagram as drawn below:

Number of students haven taken courses in Java and Linux both only

= J∩L - L∩J∩C

= 876 - 189

= 687

Number of students haven taken courses in Java and C both only

= C∩J - L∩J∩C

= 290 - 189

= 101

Number of students haven taken courses in C and Linux both only

= L∩C - L∩J∩C

= 231 - 189

= 42

Therefore,

Number of students only in Java = 1876 - 687 - 189 - 101 = 899

Number of students only in Linux = 999 - 687 - 189 - 42 = 81

Number of students only in C = 345 - 42 - 189 - 101 = 13

So,

Number of students who have not taken a course in any of these three subjects

= 2504 - 899 - 81 - 13 - 687 - 189 - 101 - 42

= 492

Hence, the students who have not taken a course in any of these three subjects = 492.