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Answer:
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.
