In a class of 80 students studying for a sessional examination, 34 students study English, 29 studies History while 42 study Geography. 12 study English and History, 14 studies Geography and History and 8 study English and Geography while 4 students did not study any of the three subjects.
i. Represent this in a Venn diagram
ii. How many students study the three subjects?
iii. How many students study any combination of two subjects only?
To represent this information in a Venn diagram, we can draw three overlapping circles, one for each subject: English, History, and Geography.
ii. Based on the given information, we know that there are 80 students in total, and 4 of them did not study any of the three subjects. Therefore, the number of students who study at least one subject is 80 - 4 = 76.
To find the number of students who study all three subjects, we start by adding the number of students who study each subject:
34 (English) + 29 (History) + 42 (Geography) = 105.
But this includes all the students who study any two subjects, so we need to subtract those students twice.
From the information given, we know:
- 12 students study English and History
- 14 students study Geography and History
- 8 students study English and Geography
So, we subtract 12 + 14 + 8 = 34 twice from the total number of students who study at least one subject:
105 - 34 - 34 = 37.
Therefore, the number of students who study all three subjects is 37.
iii. To find the number of students who study any combination of two subjects only, we take the total number of students who study at least one subject and subtract the number of students who study all three subjects:
76 - 37 = 39.
Therefore, there are 39 students who study any combination of two subjects only.