In a class of 30 students, 18 play basketball and 10 play both basketball and football. How many play football?

Instruction: Use the given information to calculate how many students play football.

Context: This question assesses the candidate's ability to apply set theory and basic arithmetic to solve a problem.

Updated

Example Answer

The information does not determine one total. Of the 18 basketball players, 10 also play football, leaving eight who play only basketball. The other 12 students could play football or neither sport. So the number of football players can be any whole number from 10 through 22.

If the interviewer adds that every student plays at least one of the two sports, then all 12 outside basketball must play football. The total would be 10 plus 12, or 22. Without that extra condition, 22 is only the maximum.

Why this works

Inclusion–exclusion gives |B ∪ F| = 18 + |F| − 10. The class size is 30, but the union need not include the whole class. Equivalently, football players + students playing neither = 22.

Follow-up to prepare for

If five students play neither sport, how many play football? Seventeen.

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