In a survey involving 60 students, it was found that 26 like Chemistry, 24 like Physics, 18 like Mathematics, 12 both Chemistry and Physics, 10 Chemistry and Mathematics, 10 Physics and Mathematics and 15 none of the three subjects. Find the number of students that like all the three subjects.
Question
In a survey involving 60 students, it was found that 26 like Chemistry, 24 like Physics, 18 like Mathematics, 12 both Chemistry and Physics, 10 Chemistry and Mathematics, 10 Physics and Mathematics and 15 none of the three subjects. Find the number of students that like all the three subjects.
Solution
To find the number of students that like all three subjects, we need to consider the students who like two subjects.
We know that:
- 12 students like both Chemistry and Physics
- 10 students like both Chemistry and Mathematics
- 10 students like both Physics and Mathematics
However, these numbers include the students who like all three subjects. To find the number of students who like all three subjects, we need to subtract the total number of students who like two subjects from the total number of students who like each subject.
So, we have:
- 26 (Chemistry) + 24 (Physics) + 18 (Mathematics) - 12 (Chemistry and Physics) - 10 (Chemistry and Mathematics) - 10 (Physics and Mathematics) = 36
But this number includes the students who like all three subjects twice. So, we need to add them back once:
- 36 + x = 60 (total students) - 15 (students who don't like any of the subjects)
Solving for x gives:
- x = 60 - 15 - 36 = 9
So, 9 students like all three subjects.
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