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In the triangle shown, 3 points are marked on side AB, 4 on side BC and 5 on side CA (none at a corner). How many triangles have all three corners among these 12 points?

Competition practicePermutations & Combinations
  • A205
  • B220
  • C210
  • D60

Step-by-Step Solution

All triples: . Triples from one side are straight lines: . Triangles .
Answer: A) 205

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