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Exercise 480Combinatorics › Inclusion-exclusionHigh schoolAdded 3 Nov 2026

Counting complement via IE

#complement#IE#at least one

Statement

Among 5050 students, 3030 play football, 2525 play basketball, 1515 play both. How many play neither?

Hint

Compute union first, then subtract from total.

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Solution

Union. 30+25−15=4030+25-15=40.

Complement. 50−40=1050-40=10.

Conclusion. 1010 students play neither.