# 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...

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.

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### 1 Answer

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

math/english -1

math/biology -1

english/biology -3 ** Note that there are 5 who take 2 classes**

all three -10

total: 37

(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.**