in a class of 60 students

Question

In a class of 60 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose to raise his or her hand. Eight hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 57 hands raised. How many students have piercings both on their ears and their noses?

Answer 1

8 had nose

52 did not have nose

so 5 had to have both