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Exercise 1721Combinatorics › Inclusion-exclusionL1Added 3 Nov 2026

A multi-property application

#IE#application#multi

Statement

Among 100100 people, 4040 are left-handed, 3030 are blue-eyed, 2525 are tall, 2020 are left-handed and blue-eyed, 1515 are left-handed and tall, 1010 are blue-eyed and tall, 55 are all three. How many have at least one of these traits?

Hint

IE with three sets.

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Solution

Union. 40+30+25−20−15−10+5=5540+30+25-20-15-10+5=55.

Conclusion. 5555 people have at least one trait.