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?
A) 11
B) 15
C) 2
D) 3

Question

Quizplus · Accepted Answer

Using the principle of inclusion-exclusion, the number of backpacks containing at least one item is calculated as follows: 23 + 27 + 21 - 15 - 12 - 18 + 10 = 36. Therefore, the number of backpacks containing none of the items is 38 - 36 = 2.

Upon Examining the Contents of 38 Backpacks, It Was Found