Q23.In a library 25 students are reading books.It was found that 15 students are reading mathematics,12 reading Physics and 11 reading Chemistry,5 students reading both mathematics and chemistry,9 students reading both physics and mathematics and 4 students reading physics andchemistry and 3 students reading all the three subjects. Calculate (i) The number of students reading only chemistry is (ii) The number of students reading only one subject is (iii) The number of students reading at least one subject is (iv) The number of students reading none of the subject is
Answers
Given : In a library 25 students are reading books.
15 students are reading mathematics,
12 reading Physics and 11 reading Chemistry,
5 students reading both mathematics and chemistry,
9 students reading both physics and mathematics and
4 students reading physics and chemistry and
3 students reading all the three subjects.
To Find : (i) The number of students reading only chemistry is
(ii) The number of students reading only one subject is
(iii) The number of students reading at least one subject is
(iv) The number of students reading none of the subject is
Solution:
Total = 25
n(M) = 15
n(P) = 12
n(C) = 11
n ( M ∩ C) = 5
n ( P ∩ M) = 9
n ( P ∩ C) = 4
n ( M ∩ P ∩ C) = 3
n( None ) = ?
Total = n(M) + n(P) + n(C) - n ( M ∩ C) - n ( P ∩ M) - n ( P ∩ C) + n ( M ∩ P ∩ C) + n(None)
25 = 15 + 12 + 11 - 5 - 9 - 4 + 3 + n( None )
=> n( None ) = 2
Hence The number of students reading none of the subject is 2
The number of students reading only chemistry is
= n(C) - n ( M ∩ C) - n ( P ∩ C) + n ( M ∩ P ∩ C)
= 11 - 5 - 4 + 3
= 5
Similarly Maths only = 4
Similarly Physics only = 2
The number of students reading only one subject is
= 5 + 4 +2
= 11
The number of students reading at least one subject is
= Total - None
25 - 2
= 23
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