In a class of 45 students it is know that 24 of them do Art 20 do chemistry and 22 do Biology. All the students do at least one of the three subjects. 3 do all the three subjects. Write 7 do Art and Biology 6 do Art and chemistry but not biology and 6 do chemistry and Biology. How many students do 1.Biology only 2.chemistry only 3.Art only 4.Two subject only
To find the number of students in each category, we can use the principle of inclusion-exclusion.
First, let's calculate the number of students in each subject:
1. Biology:
- We know that 22 students do Biology.
- From the given information, we also know that 3 students do all three subjects, and 6 do chemistry and Biology. Therefore, to find the number of students doing only Biology, we subtract the number of students doing both Chemistry and Biology from the total number of Biology students: 22 - 6 = 16 students do Biology only.
2. Chemistry:
- We know that 20 students do Chemistry.
- From the given information, we know that 3 students do all three subjects and 6 do Art and Chemistry but not Biology. Therefore, to find the number of students doing only Chemistry, we subtract the number of students doing both Art and Chemistry (but not Biology) from the total number of Chemistry students: 20 - 6 = 14 students do Chemistry only.
3. Art:
- We know that 24 students do Art.
- From the given information, we know that 3 students do all three subjects, 6 do Art and Chemistry but not Biology, and 7 do Art and Biology. Therefore, to find the number of students doing only Art, we subtract the number of students doing both Art and Chemistry (but not Biology) and those doing both Art and Biology from the total number of Art students: 24 - 6 - 7 = 11 students do Art only.
4. Two subjects only:
- To find the number of students who do two subjects only, we need to add up the students who do each subject combination (Art and Chemistry, Art and Biology, Chemistry and Biology) and subtract the students who do all three subjects.
- Art and Chemistry only: 6 students
- Art and Biology only: 7 students
- Chemistry and Biology only: 6 students
- Subtract the students who do all three subjects: 3 students
- Total number of students who do exactly two subjects: 6 + 7 + 6 - 3 = 16 students.
Therefore, the breakdown of the number of students in each category is:
1. Biology only: 16 students
2. Chemistry only: 14 students
3. Art only: 11 students
4. Two subjects only: 16 students