in a class of 60 students 30 like maths 25 like physics 30 like chemistry. if 10 like both physics and maths 5 like maths and chem and 5 like phy & chem and 3 like all the subjects. find student like none of subject of if
100 students were surveyed
Pls can u explain
To find the number of students who like none of the subjects, we can make use of the principle of inclusion-exclusion.
Let's break down the given information:
- Number of students who like math, denoted by M = 30.
- Number of students who like physics, denoted by P = 25.
- Number of students who like chemistry, denoted by C = 30.
- Number of students who like both math and physics, denoted by M∩P = 10.
- Number of students who like both math and chemistry, denoted by M∩C = 5.
- Number of students who like both physics and chemistry, denoted by P∩C = 5.
- Number of students who like all three subjects, denoted by M∩P∩C = 3.
Now, using the principle of inclusion-exclusion, we can calculate the number of students who like none of the subjects:
Number of students who like none of the subjects = Total number of students - (M + P + C) + (M∩P + M∩C + P∩C) - M∩P∩C
Total number of students surveyed = 100
Let's substitute the values into the equation:
Number of students who like none of the subjects = 100 - (30 + 25 + 30) + (10 + 5 + 5) - 3
= 100 - 85 + 20 - 3
= 32
Therefore, 32 students like none of the subjects.