Items with no defect

#IE#complement#no defect

Statement

Among $50$ items: $20$ have defect $A$ , $15$ have $B$ , $10$ have $C$ , $8$ have $A$ and $B$ , $5$ have $A$ and $C$ , $3$ have $B$ and $C$ , $2$ have all three. How many have no defect?

Hint

Union first, then complement.

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Solution

Union. $20+15+10-8-5-3+2=31$ .

Complement. $50-31=19$ .

Conclusion. $19$ items have no defect.

Items with no defect

Statement

Solution

More problems in Inclusion-exclusion