Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained none of the three writing instruments?

Question

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items.  How many backpacks contained none of the three writing instruments?

3
       11
       2
       15

I came up with 2. IS that correct?

Reiny · Answer

My Venn diagram has all my circles totaling 35 , so that 3 contained none of the above

My circles contained the following entries:
Black pen: 6 5 10 2
Blue pen : 3 8 10 5
pencil : 1 2 10 8

See if that matches with yours