Number of sets

Probability Level 1

Consider the two subsets of the integers A = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } A=\{1,2,3,4,5,6,7\} and B = { 1 , 2 , 3 , 4 } . B=\{1,2,3,4\}. How many sets of integers X X satisfy

X ∩ A c = ∅ , ∣ X ∩ B ∣ = 2 ? X \cap A^c = \emptyset, \ \lvert X \cap B \rvert=2?

40 48 44 52

Sandeep Mehra by Sandeep Mehra , 23, India

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1 solution

Röhàn Särkär
Aug 1, 2014
  1. from first condition it means that X is a subset of A.
  2. X contains exactly two elements from set B.
  3. possible no. of ways of choosing exactly two no.s from set B= 4C2= 6
  4. no of ways of choosing from A-B= {5,6,7} = 2^3= 8
  5. Hence possible no of X= 6*8= 48.
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