In a class of 50 student 28,22,20 of them offer physics,chemistry and biology respectively also,4 of them offer physics and chemistry but not biology,3 offer physic and biology but not chemistry,6 offer biology and chemistry but not physics if 13 of them offer physics only how many student in class oFfer.
At least one of the subject
Non of the three subject
(i) 14 offer physics only.
13 offer chemistry only.
12 offer biology only.
3 offer phy nd chem.
2 offer phy nd biol.
5 offer chem nd biol.
1 offers all the subjects.
(ii) 0 offers none of the subjects.
Filling in the given information in a Venn diagram, I got
8 taking all three subjects
7 taking only Chemistry
6 taking only Biology
These were the only ones that required calculations, the rest were given.
Adding up all the entries in the Venn diagrams only comes to 44, thus of the 50 students 6 take none of the three subjects.
Am not getting it
To solve this problem, we can use the principle of Inclusion-Exclusion.
First, let's find the number of students who are taking at least one of the subjects.
Step 1: Find the number of students taking only Physics.
Given that 13 students offer Physics only.
Step 2: Find the number of students taking only Chemistry.
We know that 22 students offer Chemistry, but 4 of them offer Physics and Chemistry. Therefore, 22 - 4 = 18 students offer only Chemistry.
Step 3: Find the number of students taking only Biology.
We know that 20 students offer Biology, but 3 of them offer Physics and Biology, and 6 of them offer Biology and Chemistry. Therefore, 20 - 3 - 6 = 11 students offer only Biology.
Step 4: Find the number of students taking Physics and Chemistry but not Biology.
Given that 4 students offer Physics and Chemistry but not Biology.
Step 5: Find the number of students taking Physics and Biology but not Chemistry.
Given that 3 students offer Physics and Biology but not Chemistry.
Step 6: Find the number of students taking Biology and Chemistry but not Physics.
Given that 6 students offer Biology and Chemistry but not Physics.
Now, let's calculate the number of students taking at least one of the subjects:
Number of students taking at least one subject = (Number of students taking only Physics)
+ (Number of students taking only Chemistry)
+ (Number of students taking only Biology)
+ (Number of students taking Physics and Chemistry but not Biology)
+ (Number of students taking Physics and Biology but not Chemistry)
+ (Number of students taking Biology and Chemistry but not Physics)
Number of students taking at least one subject = 13 + 18 + 11 + 4 + 3 + 6 = 55.
Therefore, there are 55 students in the class who are taking at least one of the subjects.
Next, let's find the number of students who are not taking any of the three subjects.
Number of students taking none of the three subjects = Total number of students in the class - Number of students taking at least one subject
Number of students taking none of the three subjects = 50 - 55 = -5.
Since the result is negative, it means there was an error in the information provided or in the calculations. Please check the given data again, as it is not possible to have a negative number of students taking none of the three subjects.