Exercise 1002Combinatorics › Inclusion-exclusionHigh schoolAdded 3 Nov 2026

Inclusion-exclusion in a survey

#IE#survey#population

Statement

In a survey of $200$ people: $120$ drink coffee, $100$ drink tea, $80$ drink juice, $50$ drink coffee and tea, $40$ coffee and juice, $30$ tea and juice, $20$ all three. How many drink at least one?

Hint

Three-set IE.

Show solutionHide solution

Solution

Union. $120+100+80-50-40-30+20=200$ .

Conclusion. All $200$ drink at least one. None drink none.

Inclusion-exclusion in a survey

Statement

Solution

More problems in Inclusion-exclusion