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2013 AMC 10B Question 12

AMC10 · 2013 AMC 10B

Question 12

Let $ S $ be the set of sides and diagonals of a regular pentagon. A pair of elements of $ S $ are selected at random without replacement. What is the probability that the two chosen segments have the same length?
  1. $\dfrac{2}5 $
  2. $\dfrac{4}9 $
  3. $\dfrac{1}2 $
  4. $\dfrac{5}9 $
  5. $\dfrac{4}5 $