Bounds on a football and basketball survey
Bounds on a football and basketball survey
IP 2
7 marks
In a group of \(50\) students, \(32\) like football and \(28\) like basketball.
- Explain why at least \(10\) students like both sports.[2]
- Find the greatest possible number of students who like neither sport, and describe the situation in which it happens.[2]
- Given that exactly \(5\) students like neither sport, find the number who like exactly one of the two sports.[3]
Solution:
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Answer:(a) \(n(F\cap B)=60-n(F\cup B)\ge10\) (b) \(18\), when every basketball fan also likes football (c) \(30\)
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