The enrollees of 100 students were surveyed on subject they enrolled for the first sem The following data
was collected: 48 enrolled in algebra, 39 enrolled in mechanics, 35 enrolled in physics, 20 enrolled in
algebra and mechanics, 19 enrolled in algebra and physics, 22 enrolled in mechanics and physics, 10
enrolled in algebra mechanics and physics. How many students were not enrolled in any of the three
Here is a Venn Diagram of the description: the students who took none will be: n - (sum of all numbers) (where n= 100)
We can use PIE, (Principle of Inclusion - Exclusion)
We can add 48 + 39 + 35 = 122, but this is over counting since some people took 2 or even 3 classes.
From 122, we need to subtract 20 + 19 + 22 = 61.
But we need to add 10 back to count the ones who took all the classes.
61 + 10 = 71.
100 - 71 = 29
29 students did not enroll in any of the subjects.
Total students enrolled in atleast any of subjects= students enrolled in algebra+students enrolled in mechanics+students enrolled in physics-students enrolled in algebra & physics-students enrolled in algebra & mechanics-students enrolled in mechanic & physics + students enrolled in all three
Therefore students not enrolled in any of three = 100-71