In a class of 100 students, 70 like economics, 50 like accounting and 30 like management. Each students like at least one subject and 44 students like exactly two subjects. How many students study all the three subjects
Let the number of students who like all three subjects be x.
According to the principle of inclusion and exclusion:
Total students who like economics = 70
Total students who like accounting = 50
Total students who like management = 30
Total students who like exactly two subjects = 44
Total number of students = Total students who like economics + Total students who like accounting + Total students who like management - 2(Total students who like exactly two subjects) + x
100 = 70 + 50 + 30 - 2(44) + x
100 = 70 + 50 + 30 - 88 + x
100 = 140 - 88 + x
100 = 52 + x
x = 100 - 52
x = 48
Therefore, 48 students study all three subjects.