A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and Chemistry while 8 study both Physics and Biology. Equal numbers study all three subjects as those who learn none of the three. How many study all three subjects?
Can someone show me the calculation. The ans is 3.
Venn diagram problem
P only=33-18-x
B only =26-17-x
C only =25-19-x
15-x+9-x+6-x+8+10+9+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
actually
physics = 33 - (10-x) - (8-x) - x
chem = 25 - (10-x) - (9-x) - x
bio = 26 - (9-x) - (8-x) - x
physics + chem + bio = 63
63 = 30 + 9x
33/9 = x
x = 3.6....
we cant take 18 - x and subtract with 33 because its the collection of physics and chem, phy and bio students so we have to subtract the common students
18 is the sum of the physics included pair in all three pairs(10+8=18)
Venn diagram problem
P only=33-18-x
B only =26-17-x
C only =25-19-x
15-x+9-x+6-x+8+10+9+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
Why u to take 18-x
P only=33-18-x
B only =26-17-x
C only =25-19-x
16-x+7-x+6-x+8+11+4+x=63
-2x=63
X=-3
Which means you have to work with 3 in the middle
(I dont think I'm right)
To find the number of students who study all three subjects, we can start by using a principle called the Principle of Inclusion-Exclusion. This principle helps us to count the number of elements in the union of multiple sets.
In this problem, we have three sets: Physics (P), Chemistry (C), and Biology (B). We are given the following information:
- The number of students studying Physics (n(P)) is 33.
- The number of students studying Chemistry (n(C)) is 25.
- The number of students studying Biology (n(B)) is 26.
- The number of students studying Physics and Chemistry (n(P ∩ C)) is 10.
- The number of students studying Biology and Chemistry (n(B ∩ C)) is 9.
- The number of students studying Physics and Biology (n(P ∩ B)) is 8.
- The number of students studying none of the three subjects (n(P' ∩ C' ∩ B')) is equal to the number of students studying all three subjects. Let's denote this as x.
We can use the Principle of Inclusion-Exclusion to find the number of students who study all three subjects:
n(P ∪ C ∪ B) = n(P) + n(C) + n(B) - n(P ∩ C) - n(P ∩ B) - n(B ∩ C) + n(P ∩ C ∩ B)
Plugging in the given values, we have:
63 = 33 + 25 + 26 - 10 - 8 - 9 + x
Simplifying the equation, we have:
63 = 67 + x
Subtracting 67 from both sides, we get:
x = -4
Since the number of students cannot be negative, it means there was an error in the given information or statements. There cannot be a negative number of students studying all three subjects.
Hence, the given problem cannot be solved with the provided information.