Let have elements and satisfy: for any in , some contains exactly one of them. Then necessarily
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2 marks, −0.666666666666667MathematicsCombinatorics and countingBinomial coefficients and counting functionsHardabout 4 min
DSE 2015 Question 53: Combinatorics and counting
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Let S have n>1 elements and A₁,…,Aₘ⊆ S satisfy: for any x≠ y in S, some Aᵢ contains exactly one of them. Then necessarily (A) n=2^m (B) n≤2^m (C) n>2^m (D) none of the above
Also written as: Let S have n>1 elements and A_1,...,A_m subseteq S satisfy: for any x!= y in S, some A_i contains exactly one of them. Then necessarily
Combinatorics and counting has come up 24 times in 5 exams since 2009.
What this question tests
This question is on Binomial coefficients and counting functions, part of Combinatorics and counting in Mathematics.
Binomial expansions and counting maps between finite sets.
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