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In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is
- a)23
- b)56
- c)22
- d)45
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a class of 55 students, the number of students studying different s...
Let n(M)=student who studying mathematics
n(C)=student who studying chemistry
n(P)=student who studying Physics
∴n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(M∩C)=9,n(P∩C)=7,n(M∩P∩C)=4
Number of student who studying mathematics but not physic and chemistry
⇒n(M)−[(n(M∩C)+n(M∩P)]+n(M∩P∩C)
⇒23−[9+12]+4
⇒23−21+4=6
Number of student who studying chemistry but not physic and matehematics
⇒n(C)−[(n(M∩C)+n(P∩C)]+n(M∩P∩C)
⇒19−[9+7]+4
⇒19−16+4=7
Number of student who studying physics but not mathematics and chemistry
⇒n(P)−[(n(M∩P)+n(P∩C)]+n(M∩P∩C)
⇒24−[12+7]+4
⇒24−19+4=9
∴no. of student studying exactly one subject = 6+7+9 = 22.
Most Upvoted Answer
In a class of 55 students, the number of students studying different s...
Given Information:
- Total number of students in the class = 55
- Number of students studying Mathematics = 23
- Number of students studying Physics = 24
- Number of students studying Chemistry = 19
- Number of students studying Mathematics and Physics = 12
- Number of students studying Mathematics and Chemistry = 9
- Number of students studying Physics and Chemistry = 7
- Number of students studying all three subjects = 4
To Find:
The number of students who have taken exactly one subject.
Solution:
To find the number of students who have taken exactly one subject, we need to subtract the number of students who have taken more than one subject from the total number of students.
Students taking more than one subject:
To find the number of students who have taken more than one subject, we need to add the number of students studying Mathematics and Physics, Mathematics and Chemistry, and Physics and Chemistry. However, we need to subtract the number of students studying all three subjects as it has been counted twice.
Number of students studying more than one subject = (Number of students studying Mathematics and Physics) + (Number of students studying Mathematics and Chemistry) + (Number of students studying Physics and Chemistry) - (Number of students studying all three subjects)
= 12 + 9 + 7 - 4
= 24
Students taking exactly one subject:
Number of students taking exactly one subject = Total number of students - Number of students taking more than one subject
= 55 - 24
= 31
Therefore, the number of students who have taken exactly one subject is 31.
Answer:
Option c) 1
- Total number of students in the class = 55
- Number of students studying Mathematics = 23
- Number of students studying Physics = 24
- Number of students studying Chemistry = 19
- Number of students studying Mathematics and Physics = 12
- Number of students studying Mathematics and Chemistry = 9
- Number of students studying Physics and Chemistry = 7
- Number of students studying all three subjects = 4
To Find:
The number of students who have taken exactly one subject.
Solution:
To find the number of students who have taken exactly one subject, we need to subtract the number of students who have taken more than one subject from the total number of students.
Students taking more than one subject:
To find the number of students who have taken more than one subject, we need to add the number of students studying Mathematics and Physics, Mathematics and Chemistry, and Physics and Chemistry. However, we need to subtract the number of students studying all three subjects as it has been counted twice.
Number of students studying more than one subject = (Number of students studying Mathematics and Physics) + (Number of students studying Mathematics and Chemistry) + (Number of students studying Physics and Chemistry) - (Number of students studying all three subjects)
= 12 + 9 + 7 - 4
= 24
Students taking exactly one subject:
Number of students taking exactly one subject = Total number of students - Number of students taking more than one subject
= 55 - 24
= 31
Therefore, the number of students who have taken exactly one subject is 31.
Answer:
Option c) 1
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In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject isa)23b)56c)22d)45Correct answer is option 'C'. Can you explain this answer?
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