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 8 do chemistry and Biology. How many students do 1.Biology only 2.chemistry only 3.Arts only 4.Two subjects only
To find the number of students in each category, we need to use the principle of inclusion-exclusion.
1. Biology only:
We know that 22 students do Biology, including the 3 students who do all three subjects. So, the number of students who do Biology only is 22 - 3 = 19.
2. Chemistry only:
We know that 20 students do Chemistry, including the 3 students who do all three subjects. Additionally, 8 students do both Chemistry and Biology. To find the number of students who do Chemistry only, we subtract the students who do both Chemistry and Biology from the total number of Chemistry students, which gives us 20 - 8 = 12.
3. Art only:
We know that 24 students do Art, including the 3 students who do all three subjects. Additionally, 7 students do both Art and Biology, and 6 students do Art and Chemistry but not Biology. To find the number of students who do Art only, we subtract the students who do both Art and Biology and the students who do Art and Chemistry but not Biology from the total number of Art students, which gives us 24 - 7 - 6 = 11.
4. Two subjects only:
To find the number of students who do two subjects only, we need to add up the number of students who do each combination of two subjects, excluding the students who do all three subjects. From the given information, we know that there are 3 students who do all three subjects.
- Art and Biology only: Given 7 students do Art and Biology, subtract the students who do all three subjects, which gives us 7 - 3 = 4 students.
- Art and Chemistry only: Given 6 students do Art and Chemistry but not Biology, subtract the students who do all three subjects, which gives us 6 - 3 = 3 students.
- Chemistry and Biology only: Given 8 students do Chemistry and Biology, subtract the students who do all three subjects, which gives us 8 - 3 = 5 students.
Adding up the number of students who do each combination of two subjects only, we get 4 + 3 + 5 = 12 students.
So, the final breakdown is:
1. Biology only: 19 students
2. Chemistry only: 12 students
3. Art only: 11 students
4. Two subjects only: 12 students.