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There's a set $S$ with $8$ elements. How many distinct $3-$element subsets of $S$ are possible such that the intersection of any $2$ of them is not a $2-$element set?

Please help. I think its $14$. The options are :

  1. $28$
  2. $56$
  3. $112$
  4. $14$
  5. $168$
  • 1
    The question is unclear. Do you want to know the *maximum size* of such collections of 3-elements subsets, or do you want to know *how many such collections* are possible? In either case I don't think the answer appears among the given choices. Also, what makes you favor 14?2012-07-23
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    Is your reason for thinking it's 14 that you have actually found 14 such 3-element subsets? Can you show us?2012-07-23

2 Answers 2