Case Study
"In a survey of 400 students of a college it was found that 240 study mathematics, 180 study Statistics and 140 study Accounts, 80 study mathematics and Statistics, 60 study Statistics and Accounts, 100 study Accounts and mathematics and 40 study none of these subjects. On the basis of this information answer the following questions.
Q1. Find the number of students who study Accounts only.
Answers
Answer:
The number of students who study Accounts only would be 20.
Step-by-step explanation:
Let M = students who study Math,
S = students who study Statistics,
A = students who study accounts,
According to the question,
n(M) = 240, n(S) = 180, n(A) = 140, n(M∩S) = 80, n(S∩A) = 60 and n(A∩M) = 100,
Total students = 400,
In which 40 study none of these subjects,
So, n(M∪S∪A) = 400 - 40 = 360,
We know that,
n(M∪S∪A) = n(M) + n(S) + n(A) - n(M∩S) - n(S∩A) - n(A∩M) + n(M∩S∩A)
⇒ 360 = 240 + 180 + 140 - 80 - 60 - 100 + n(M∩S∩A)
⇒ 360 = 320 + n(M∩S∩A)
⇒ n(M∩S∩A) = 40,
Hence, the number of students who study Accounts only= n(A) - n(S∩A) - n(A∩M) + n(M∩S∩A)
= 140 - 60 - 100 + 40
= 20
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