In a survey of 40 students,it was found that 21had taken M, 16 had taken P and 15 had taken C,7 had taken M and C,12 had taken M and P, 5 had taken P and C and 4 had taken all the three subjects.
Based on the above information, answer the following questions :
The number of students who had taken M only is
(a) 5 (b)6 (c) 7 (d) 8
The number of students who had taken atleast one of three subjects is
(a) 40 (b) 38 (c) 34 (d) 32
(3) The number of students who had taken P and C but not M is
(a) 1 (b) 3 (c) 5 (d) 7
(4)The number of students who had taken none of the subjects is
(a) 8 (b) 2 (c) 6 (d) 0
Answers
Answer:
all are d) i know same answer I am telling you
Given : a survey of 40 students
To Find : The number of students who had taken M only
The number of students who had taken atleast one of three subjects is
The number of students who had taken P and C but not M is
The number of students who had taken none of the subjects is
Solution:
Total = 40
n(M) = 21
n(P) = 16
n(C) = 15
n ( M ∩ C) = 7
n ( M ∩ P) =12
n ( P ∩ C) = 5
n ( M ∩ P ∩ C ) = 4
Total = n(M) + n(P) + n(C) - n ( M ∩ C) - n ( M ∩ P) - n ( C ∩ P) + n ( M ∩ P ∩ C ) + none
=> 40 = 21 + 16 + 15 - 7 - 12 - 5 + 4 + none
=> none = 8
The number of students who had taken none of the subjects is 8
The number of students who had taken M
n(M) - n ( M ∩ C) - n ( M ∩ P) + n ( M ∩ P ∩ C )
= 21 - 7 - 12 + 4
= 6
The number of students who had taken atleast one of three subjects is
= Total - none
= 40 - 8
= 32
The number of students who had taken P and C but not M is
n ( C ∩ P) - n ( M ∩ P ∩ C ) = 5 - 4 = 1
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