Among 100 students, 32 study mathematics, 20 study physics, 45 study biology, 15 study mathematics and biology, 7 study mathematics and physics, 10 study physics and biology and 30 do not study any of three subjects. (a) find the number of students studying all three subjects. (b) find the number of students studying exactly one of the three subjects.
Answers
Answer:
math is large subject study
a) The number of students studying all three subjects is 5.
b) The number of students studying exactly one of the three subjects is 48.
Step-by-step explanation:
Given : Among 100 students, 32 study mathematics, 20 study physics, 45 study biology, 15 study mathematics and biology, 7 study mathematics and physics, 10 study physics and biology and 30 do not study any of three subjects.
To find :
(a) find the number of students studying all three subjects.
(b) find the number of students studying exactly one of the three subjects.
Solution :
Let M, P, B denote the set of students studying Maths, Physics and Biology respectively.
In order to find the number of students studying exactly one of the subjects, we need to draw the Venn Diagram and use it further to find the solution.
Refer the attached figure below.
(a) The number of students studying all three subjects.
The common in all is 5.
So, 5 are studying all subjects.
(b) The number of students studying exactly one of the three subjects.
7 - 5 = 2 study Maths and Physics but not all three
15 - 5 = 10 study Maths and Biology But not all three
10 - 5 = 5 study Biology and Physics But not all three
32 - (10 + 2 + 5) = 15 study Maths Only
20 - (2 + 5 + 5) = 8 study Physics Only
45 - (10 + 5 + 5) = 25 study Biology Only
Number of Students studying exactly one of the three subjects is given by,
n= 15 + 8 + 25 = 48
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