Exercise 884Combinatorics › Counting principlesOlympiadAdded 3 Nov 2026

At least one property

#inclusion-exclusion#properties#at least one

Statement

Among $100$ items, $20$ have defect $A$ , $15$ have defect $B$ , $10$ have defect $C$ , $8$ have $A$ and $B$ , $5$ have $A$ and $C$ , $3$ have $B$ and $C$ , $2$ have all three. How many have at least one defect?

Hint

IE.

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Solution

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

Conclusion. $31$ items have at least one defect.

At least one property

Statement

Solution

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