Out of 100 students; 15 passed in E...
Question
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science ;4 in English and Scien
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Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science ( ; 4 ) in English and Science ( ; 4 ) in all the three. Find
how many passed
(i) in-English and Mathematics but not in Science
(ii) in Mathematics and Science but not in English
(iii) in Mathematics only
(iv) in more than one subject only

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Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science ;4 in English and Science ;4 in all the three. Find how many passed
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Let ( mathrm{M} ) be the set of students who passed in Mathematics, ( mathrm{E} ) be the set of
students who passed in English and S be the set of students who passed
in Science.
Given ( n(U)=100 )
( n(E)=15, n(M)=12, n(S)=8 )
( mathrm{n}(mathrm{E} cap mathrm{M})=6, mathrm{n}(mathrm{M} cap mathrm{S})=7, mathrm{n}(mathrm{E} cap mathrm{S})-4, ) and ( mathrm{n}(mathrm{E} cap mathrm{M} cap mathrm{S})=4 )
From the figure, we have
[
begin{array}{ll}
a=n(E cap M cap S)=4
a+d=n(M cap S)=7
therefore=3
a+b=n(M cap E)=6
therefore quad b=2
a+c=n(S cap E)=4
therefore quad c=0
a+b+d+e=n(M)=12
therefore quad 4+2+3+e=12
therefore=3
end{array}
]
( a+b+c+g=15 )
( therefore quad 4+2+0+g=n(E)=15 )
( therefore quad g=9 )
( a+c+d+f=n(S)=8 )
( therefore quad 4+0+3+f=8 )
( therefore quad f=1 )
Number of students passed in English and Mathematics but not in
Science ( =b=2 )
(ii) Number of students passed in Mathematics and Science but not in
English ( =d=3 )
(iii) Number of students passed in Mathematics only ( =mathrm{e}=3 )
(iv) Number of students passed in more than one subject ( =a+b+c+d )
( =4+2+0+3=9 )

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