Among 18 students in a room, 7 study mathematics, 10 study science, and 10 study computer programming. Also, 3 study mathematics and science, 4 study mathematics and computer programming, and 5 study science and computer programming. We know that 1 student studies all three subjects. How many of these students study none of the three subjects?

3 students study none of the three subjects

Step-by-step explanation:

The Venn diagram representing the situation is shown in the attached photo.

M represents the sub set of mathematics students.

S represents the sub set of science students.

CP represents the sub set of computer programming students.

From the diagram,

The number of students studying mathematics and science only is

3 - 1 = 2

The number of students studying mathematics and computer programming only is

4 - 1 = 3

The number of students studying science and computer programming only is

5 - 1 = 4

The number of students studying mathematics only is

7 - (2 + 1 + 3) = 1

The number of students studying mathematics only is

10 - (2 + 1 + 4) = 3

The number of students studying computer programming only is

10 - (3 + 1 + 4) = 2

Let x represent the number of students that study none of the three subjects. Since the total number of students is 18, it means that

2 + 3 + 4 + 1 + 3 + 2 + x = 18

15 + x = 18

x = 18 - 15 = 3

what are the options? ?

step-by-step explanation: