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A polygon has 12 sides. Counting the combinations of two vertices that are not adjacent, how many diagonals does the polygon have?

Competition practiceProbability & Permutation
  • A66
  • B54
  • C44
  • D36

Step-by-Step Solution

Any 2 of the 12 vertices can be joined in C(12,2) = 66 ways, but 12 of those joins are sides of the polygon. Diagonals = 66 - 12 = 54. Choosing 66 forgets to remove the sides.
Answer: B) 54

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