SOLUTION: A class of 40 students was each required to having the text books in each of economics, geography and mathematics . It was revealed that 20 had economics books , 24 had geography b

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Question 1108451: A class of 40 students was each required to having the text books in each of economics, geography and mathematics . It was revealed that 20 had economics books , 24 had geography books and 22 had mathematics books. 16 students had two of the three books. Every student had at least on of the three books.
a. Illustrate the information on a Venn diagram
b. Find the number of students who had all three books.
Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
Let the 3 circles represent people who have each of the books.
People who have two or three of the books
are represented by the regions labeled with letters,
and those letters represent the numbers of students in each region,
representing the number of students that has all 3 books,
represents the number of students that has exactly 2 of the books.
If we add the contents of all 3 circles, we are counting 16 people twice,and we are counting 3 times.
To get the right count we have to subtract the extra countings, so