There are 120pupil in a class.
18 takes math,21 english and 23 biology. 5 takes exactly the two subjects. Only 1 pupil takes math and english. 6 pupil takes math only. 10 pupil takes 3 of the subjects. Find out,the number of students
a)Who have taken none of the subjects.
b)Takes english only.
c)takes biology only.
There are 10 students who take all three classes, exactly 1 student who takes english and math, and 6 students who take only math. Since 18 total students take math, and we have accounted for 17, there is one student who takes math and biology.
Since there are 5 students who take exactly 2 classes, and we have accounted for 2 of them (1 takes math/english and the other math/biology), there are 3 students who take english and biology.
Now 1 student takes mathand biology, 10 students take all three classes, and 3 students take biology and english. We have accounted for 14 of the students who take biology; since there are 23 biology students, 9 must take only biology.
We have 1 student who takes english and math, 10 students who take all three, and 3 students who take english and biology. We have accounted for 14 english students; since there are a total of 21, then there are 7 students who take english only.
There are a total of 37 students accounted for:
math only -6
biology only -9
english only -7
english/biology -3 ** Note that there are 5 who take 2 classes**
all three -10
(a) Since there are a total of 120 students, and we have accounted for 37 there are 120-37=83 students who are in none of the listed classes.
(b) As found above, there are 7 students who take english only.
(c) As found above, there are 9 students who take biology only.