Answer to Question #185892 in Discrete Mathematics for Aroosha ch

Question

In a high school, 50 students are surveyed and asked about the interest of the student. 23 students interested in English subject, 14 interested in Mathematics, and 11 in Urdu, 6 is in English an mathematics, 4 is in English and Urdu , and 5 is in English and Urdu. 15 students not interested in any subject. How many students interested in 3 subjects? Also represent your answer by using Venn diagram.

Answer 1

Solution:

A piece of the given information is incorrect as the number of students 'English and Urdu' is given twice with different numbers. So, we assume, 4 is in Mathematics and Urdu, and 5 is in English and Urdu.

Notation:

U - Urdu, M - mathematics, E - english

Let the number of students interested in all 3 subjects be $a$.

Then, making its Venn diagram:

So, $12+a+4+a+2+a+6-a+4-a+5-a+a+15=50$

$\Rightarrow 47+a=50 \\\Rightarrow a=3$

Thus, only 3 students are interested in all 3 subjects.

Now, Venn diagram with a = 3: