In a survey of 25 students it was found that 15 had taken maths,12 had taken physics,and 11 had taken chemistry, 5 had taken math and chemistry,9 had taken math and physics, 4 had taken physics and chemistry,and three had taken all the three subject find the no of students that taken .Only chemistry.only math,only physics,physics and chemistry but not math,math and physics but not chemistry,only one of the subject,at least one of the subject ,none of the subject .
Answers
This problem can be solved easily using Venn diagram.
Step-by-step explanation:
1. Draw 3 circles within a rectangular box, with all three circles representing one subject each viz., Mathematics, Chemistry and Physics and rectangular box representing all 25 students. The circles must be intersecting each other as there are students who have opted 1 of 3, 2 of 3 and 3 of all 3 subjects.
2. Start filling with number of students provided from those who have opted all three subjects, that is 3 according to problem.
3. Then fill the number of students who have opted 2 of 3 subjects. But remember that we have already filled no. of students who have opted all 3 subjects. Filling for students with 2 subjects will also include them. So we need to subtract 3 from given no. of students choosing 2 subjects.
For example : No. of students opting Maths and Chemistry is 5 which includes 3 students with all three subjects and 2 with only chemistry and maths. Therefore no. of students opting only chemistry and maths comes out to be 2 only.
4. Now following the same procedure a above we can fill the no. of students with one subject only.
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By doing so we get student with :
Only Chemistry : 5
Only Maths : 4
Only Physics : 2
Physics and Chemistry but not Maths : 8
Maths and Physics but not Chemistry : 12
Only one of the subjects : 11
At least one of the subject : 23
None of the subjects : 2
