In a group of 40 students, 20 play football, 19 play volleyball, and 15 play exactly one of these two sports. How many students do not practice football and volleyball?
(a) 7
(b) 5
(c) 13
(d) 9
(e) 10
Let $x$ be the number of students who practice both sports simultaneously. Therefore, the number of students who practice only football is $20-x$ and those who practice only volleyball is $19-x$. Thus, the students who practice exactly one sport are

$$
(20-x)+(19-x)=15
$$

It follows that $x=12$ and we will have that the students who practice some sport are

$$
20+(19-x)=27
$$

Therefore, those who do not practice any sport are 13. The correct option is (c).