    Question

# A class has 175 students. the followng data shows the number of students obtaining one or more subjects. mathematics 100; physics 70; chemistry 40; mathematics and physics 30; mathematics and chemistry 28; physics and chemistry 23; mathematics, physics and chemistry 18. how many students have offered mathematics alone? (1) 35 (2) 48 (3) 60 (4) 22

Open in App
Solution

## Solution:- Let M, P and C represents the sets of the students who studied mathematics, physics and chemistry respectively. Given : n(M) = 100 ; n(P) = 70 and n(C) = 40 n(M∩P) = 30 ; n(M∩C) = 28 and n(P∩C) = 23 and n(M∩P∩C) = 18 n(M∪P∪C) = n(M) + n(P) + n(C) - n(M∩P) - n(M∩C) - n(P∩C) + n(M∩P∩C) = 100 + 70 + 40 - 30 - 28 - 23 + 18 = 228 - 81 = 147 So, the number of students who any of the subjects = 147 Therefore, the number of students who have not any of these three subjects = 175 - 147 = 28 students. Thus, 28 students have not offered any of these three subjects. Now, Number of students who are enrolled in mathematics alone = n(M) - n(M∩P) - n(M∩C) + n(M∩P∩C) = 100 - 30 - 28 +18 = 118 - 58 = 60 students enrolled in mathematics alone.  Suggest Corrections  11      Similar questions  Related Videos   Venn Diagrams
MATHEMATICS
Watch in App  Explore more