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A team of four players is to be formed from seven players - three males (a, b, c) and four females (m, n, o, p). The team must have at least two males and must adhere to the following restrictions: b cannot play with m, c cannot play with p, and a cannot play with o. Which statement must be false?
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Solution: Step 1: Evaluate each statement based on given restrictions. 1. b and p cannot be selected together - Not directly supported or contradicted. 2. c and o cannot be selected together - Not directly supported. 3. c and n cannot be selected together - This must be false as there is no restriction involving c and n. Step 2: Analyze restrictions. Given restrictions: b and m, c and p, a and o. No restriction between c and n. Step 3: Conclusion. The statement that 'c and n cannot be selected together' must be false as it claims a restriction where none exists. Thus, the answer is: c and n cannot be selected together.
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