In a class of47 student ,31 study physics ,26 study chemistry and 16 study Biology . 3study all the three subjects, 2 study chemistry and biology only and 6study Biology only . Find
1. Chemistry only
2. Only one subject
3. Only two subjects
To find the number of students studying chemistry only, we need to subtract the number of students studying all three subjects and the number of students studying chemistry and biology only from the total number of students studying chemistry.
Number of students studying chemistry only = Total number of students studying chemistry - Number of students studying all three subjects - Number of students studying chemistry and biology only
= 26 - 3 - 2
= 21
To find the number of students studying only one subject, we need to sum the number of students studying physics only, chemistry only, and biology only.
Number of students studying only one subject = Number of students studying physics only + Number of students studying chemistry only + Number of students studying biology only
= (31 - 3) + 21 + (16 - 3 + 2 + 6)
= 28 + 21 + 21
= 70
To find the number of students studying only two subjects, we need to subtract the number of students studying all three subjects and the number of students studying only one subject from the total number of students.
Number of students studying only two subjects = Total number of students - Number of students studying all three subjects - Number of students studying only one subject
= 47 - 3 - 70
= 47 - 73
= -26
Note: The result is negative because it is not possible for the number of students studying only two subjects to be negative. This means that there might be an error in the given information or calculations.
To find the number of students studying each combination of subjects, we can use a Venn diagram and fill in the given information.
Let's label the three circles as P for Physics, C for Chemistry, and B for Biology.
1. To find the number of students studying only Chemistry, we need to find the count of students in the C circle who are not in any other circles. According to the information given, 26 students study Chemistry, 3 students study all three subjects, and 2 students study Chemistry and Biology only. Therefore, the number of students studying only Chemistry is:
26 - 3 - 2 = 21 students.
2. To find the number of students studying only one subject, we need to add up the students studying each subject individually, minus the students studying all three subjects. Let's calculate this for each subject:
- Physics only: 31 - 3 = 28 students.
- Chemistry only: 21 students. (calculated in step 1)
- Biology only: 6 students.
Now, let's sum up the students studying only one subject:
28 + 21 + 6 = 55 students.
3. To find the number of students studying only two subjects, we can sum up the students studying each combination of two subjects:
- Physics and Chemistry: 3 students. (given)
- Physics and Biology: There are no specific numbers given for this combination, so we need to calculate it. We can subtract the number of students studying only one subject (calculated in step 2) from the total number of students studying Biology:
31 - 6 = 25 students.
- Chemistry and Biology: 2 students. (given)
Now, let's sum up the students studying only two subjects:
3 + 25 + 2 = 30 students.
To summarize:
1. Chemistry only: 21 students.
2. Only one subject: 55 students.
3. Only two subjects: 30 students.