word problem

Question

Twenty students in the homeroom class are signing up for fine arts electives. So far, 5 students have signed up for band, 6 have signed up for drama, and 12 signed up for art. There are 3 students who signed up for both drama and art, 2 students who signed up for both art and band and 1 student who signed up for all three. How many students have not yet registered for an elective ?

Answer 1

Art only  8

Art & Band only 1

Art & Drama only 2

Art & Band & Drama 1     TOTAL 12 in Art

 

Band only 3   (Note 5 in Band, total; see above)

 

Drama only 3 because 6 total in Drama, 3 of whom were already counted above.

 

TOTAL of all counts in all distinct parts of semi-overlapping 3 circles labeled ART, BAND, DRAMA: 18 (make a Venn diagram).

 

Since there are 20 students in all, there must be TWO who have not yet chosen their Elective(s).