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?

2

Explanation:

Given

Total bags=38

No of bags containing black pen is

No of bags containing blue pen

No of bags containing  pencil

no of bags containing both Black pen & blue

no of bags containing both Black pen & Pencil

no of bags containing both Blue pen & Pencil

no of bags containing all

using Venn diagram

and we know

Therefore there are 2 bags which are empty.

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