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2008 AMC 12B Question 22

AMC12 · 2008 AMC 12B

Question 22

A parking lot has $16$ spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers choose their spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires $2$ adjacent spaces. What is the probability that she is able to park?
  1. $\dfrac{11}{20}$
  2. $\dfrac{4}{7}$
  3. $\dfrac{81}{140}$
  4. $\dfrac{3}{5}$
  5. $\dfrac{17}{28}$