GATE | GATE-IT-2004 | Question 2

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Data Structures and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.How many students have not taken any of the three courses?

(A) 15
(B) 20
(C) 25
(D) 35


Answer: (C)

Explanation:

P(AUBUC)=P(A)+P(B)+P(C)- P(A∩B)-P(A∩C)- P(B∩C)+P(A∩B∩C)

125+85+65-50−35−30+15 =175

No of students not taking any courses-> 200−175=25

So C is the Answer.

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