Quality control in a factory pulls 40 parts with paint packa

Quality control in a factory pulls 40 parts with paint, packaging, or electronics defects from an assembly line. Of these, 28 had a paint defect, 17 had a packaging defect, 13 had an electronics defect, 6 had both paint and packaging defects, 7 had both packaging and electronics defects, and 10 had both paint and electronics defects. Did any part have all three types of defect?

Solution

Given
Quality control in a factory pulls 40 parts with defects from an assembly line.
Out of the 40
Pain defects are 28
Packaging defect are 17
Electronics defect are 13
Both Paint and Packaging defects are 6
Both Packaging and Electronics defects are 7
Both Paint and Electronics defects are 10
Let \'x\' be the number of parts which have all the three types of defects.
So now,
40 = 28+17+13-6-7-10+x

40 = 35+x

Now x = 440-35

x =5

So 3 parts have all three types of defects.