If a class of 40 students includes 18 who play basketball and 15 who play football, with 7 playing both, how many students play at least one of the sports?

Question

BlackTom AI · Accepted Answer

We start by identifying what the question asks: how many students play at least one of the two sports (basketball or football).
Option 1: 34. This would imply |A ∪ B| = 34. Using inclusion-exclusion, |A ∪ B| = |A| + |B| − |A ∩ B| = 18 + 15 − x. To get 34, x would need to be −1, which is impossible. Therefore 34 cannot be the correct count.
Option 2: 28. If 28 were the union size, then the intersection would need to satisfy 18 + 15 − |A ∩ B| = 28, so |A ∩ B| = 5. But the problem states that 7 students play both, so 28 would misrepresent the overlap and is inconsistent with the given data.
Option 3: 40. This would indicate that every student plays at least one sport. However, the total class size is 40, and since only 18 play basketball and 15 play football with 7 overlapping, the union size is 18 + 15 − 7 = 26, leaving 14 students who play neither. Hence 40 cannot be correct.
Option 4: 26. Here, applying inclusion-exclusion: 18 (basketball) + 15 (football) − 7 (both) = 26 students playing at least one sport. This aligns with the given numbers and the overlap, so it is consistent and correctly accounts for those who are counted twice.

If a class of 40 students includes 18 who play basketball and 15 who play football, with 7 playing both, how many students play at least one of the sports?单项选择题

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