In a class of 80 students, 67 like History, 62 like Geography and 35 like Civics. It may be possible that some students do not like any of these three subjects. Then the difference between the maximum and minimum possible number of students who like all the three subjects is
Question
In a class of 80 students, 67 like History, 62 like Geography and 35 like Civics. It may be possible that some students do not like any of these three subjects. Then the difference between the maximum and minimum possible number of students who like all the three subjects is
Solution
To solve this problem, we need to find the maximum and minimum possible number of students who like all three subjects, and then find the difference between these two numbers.
Step 1: Find the maximum possible number of students who like all three subjects.
The maximum possible number of students who like all three subjects is the minimum number of students who like any one of the subjects. This is because it's possible that the group of students who like one subject is entirely contained within the groups of students who like the other two subjects. In this case, the minimum number of students who like any one subject is 35 (Civics). So, the maximum possible number of students who like all three subjects is 35.
Step 2: Find the minimum possible number of students who like all three subjects.
The minimum possible number of students who like all three subjects can be found by adding the number of students who like each subject and subtracting the total number of students. If this number is less than zero, then the minimum possible number of students who like all three subjects is zero (since we can't have a negative number of students).
Number of students who like History = 67 Number of students who like Geography = 62 Number of students who like Civics = 35 Total number of students = 80
So, the minimum possible number of students who like all three subjects is 67 + 62 + 35 - 80 = 84. Since this number is greater than zero, the minimum possible number of students who like all three subjects is 84.
Step 3: Find the difference between the maximum and minimum possible number of students who like all three subjects.
The difference between the maximum and minimum possible number of students who like all three subjects is 35 - 84 = -49. Since we can't have a negative difference, we take the absolute value of this number, which is 49.
So, the difference between the maximum and minimum possible number of students who like all three subjects is 49.
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