In the class of 45 students it is known that 24 of them do art 20 do chemistry 22 do biology all of the students do at least one of the three subject while 7 do art and biology 6 do art and chemistry but only not biology and do chemistry and biology
How many do
1, biology only or chemistry only or art only
2, two subject
make a Venn diagram
1. To find the number of students who do only biology, only chemistry, or only art, we can subtract the number of students who do two or three subjects from the total number of students.
Total number of students = 45
Number of students who do at least one subject = 45
Number of students who do two or three subjects = 7 (art and biology) + 6 (art and chemistry) + 6 (chemistry and biology) = 19
Number of students who do only biology, chemistry, or art = Total number of students - Number of students who do two or three subjects
= 45 - 19
= 26
So, there are 26 students who do biology only, chemistry only, or art only.
2. To find the number of students who do two subjects, we add up the number of students who do each combination of two subjects.
Number of students who do art and biology = 7
Number of students who do art and chemistry = 6
Number of students who do chemistry and biology = 6
Number of students who do two subjects = Number of students who do art and biology + Number of students who do art and chemistry + Number of students who do chemistry and biology
= 7 + 6 + 6
= 19
So, there are 19 students who do two subjects.
To find the number of students who do biology only, chemistry only, or art only, we can subtract the number of students who do two or three subjects from the total number of students who do at least one subject.
1. Biology only or Chemistry only or Art only:
To calculate the number of students who do only one subject, we need to subtract the numbers of students who do two or more subjects from the total number of students.
Total number of students = 45
Students who do two or three subjects = 7 + 6 + 6 = 19
Number of students who do only one subject = Total number of students - Students who do two or more subjects
Number of students who do only one subject = 45 - 19 = 26
Therefore, there are 26 students who do biology only, chemistry only, or art only.
2. Two subjects:
To find the number of students who do two subjects, we can sum up the numbers of students who do any two of the three subjects.
Number of students who do two subjects = Students who do art and biology + Students who do art and chemistry + Students who do chemistry and biology
Number of students who do two subjects = 7 + 6 + 6 = 19
Therefore, there are 19 students who do two subjects.