In a class of 36 students, 18 offers chemistry, 16 offers physics, 22 offers mathematics, 6 offered all the 3 subjects, 3 offers chemistry and physics only, 5 offer physics only and at least each student offered one of the subjects. Find the number of students who offered,
a. Chemistry only
b. Only one subject
c. Only two subjects
To solve the problem, we can use the principle of inclusion-exclusion.
a. To find the number of students who offered chemistry only, we need to subtract the number of students who offered both chemistry and another subject from the total number of students who offered chemistry:
Number of students who offered chemistry only = Number of students who offered chemistry - Number of students who offered chemistry and another subject
Number of students who offered chemistry only = 18 - (3 + 6)
Number of students who offered chemistry only = 9
Therefore, 9 students offered chemistry only.
b. To find the number of students who offered only one subject, we need to add up the number of students who offered each subject only:
Number of students who offered only one subject = Number of students who offered mathematics only + Number of students who offered physics only + Number of students who offered chemistry only
Number of students who offered only one subject = (22 - 6) + (16 - 3 - 6) + (18 - 3 - 6)
Number of students who offered only one subject = 16
Therefore, 16 students offered only one subject.
c. To find the number of students who offered only two subjects, we need to subtract the number of students who offered only one subject from the total number of students who offered at least two subjects:
Number of students who offered only two subjects = Number of students who offered at least two subjects - Number of students who offered only one subject
Number of students who offered only two subjects = (6 + 3 + 5) - 16
Number of students who offered only two subjects = 2
Therefore, 2 students offered only two subjects.