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2010 AMC 12A Question 16

AMC12 · 2010 AMC 12A

Question 16

Bernardo randomly picks $3$ distinct numbers from the set $$
\{1,2,3,4,5,6,7,8,9\}
$$ and arranges them in descending order to form a $3$-digit number. Silvia randomly picks $3$ distinct numbers from the set $$
\{1,2,3,4,5,6,7,8\}
$$ and also arranges them in descending order to form a $3$-digit number. What is the probability that Bernardo’s number is larger than Silvia’s number?
  1. $\dfrac{47}{72}$
  2. $\dfrac{37}{56}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{49}{72}$
  5. $\dfrac{39}{56}$