In a college that has 100 arts students, there are 5 optional subjects among History, Music, Dance, Debate and Photography to choose from. 99% of them choose at least one subject, 49% choose at least 2 subjects, 24% choose at least 3 subjects, 14% choose at least 4 subjects and 4% choose all the subjects. What is the sum of number of students who choose exactly three subjects and who choose exactly 4 subjects?

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Solution

The correct option is D
20

X=100

One =A, Two =B, Tree=C, Four= D, Five =E

Atleast 1 = A+B+C+D+E = 99----------------------(1)

Atleast 2= B+C+D+E=49-----------------------------(2)

Atleast 3= C+D+E= 24--------------------------------(3)

Atleast 4= D+E=14------------------------------------(4)

Atleast 5= E=4-------------------------------------------(5)

4-5= D+E-E = D= 14-4=10 (Exactly 4 = 10)

3-4= C+D+E-(D+E) =C = 24-14=10 (Exactly 3 =10)

Total = 10+10=20

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