In a school of 120 students, 72 are enrolled in a music course, 36 are enrolled in a dance course, and 18 students are enrolled in both courses.

Consider the following statements:

Statement I: The number of students enrolled in at least one of the two courses is 90.
Statement II: The number of students enrolled in neither music nor dance courses is 30.
Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

In a school of 120 students, 72 are enrolled in a music course, 36 are enrolled in a dance course, and 18 students are enrolled in both courses.

Consider the following statements:

Statement I: The number of students enrolled in at least one of the two courses is 90.
Statement II: The number of students enrolled in neither music nor dance courses is 30.
Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

Using the principle of inclusion and exclusion:

Students enrolled in at least one course =
= (Music) + (Dance) &minus; (Both)
= 72 + 36 &minus; 18 = 90

Total students = 120
Students in neither course = 120 &minus; 90 = 30

Statement I: 90 students are enrolled in at least one course &rarr; Correct

Statement II: 30 students are enrolled in neither &rarr; Correct

Hence, option c is correct.

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