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AMC10 2027 - Self-practice Set 5 Question 2

AMC10 · AMC10 2027 - Self-practice Set 5

Question 2

Bernardo uniformly selects three distinct digits from $\{1,2,\ldots,9\}$ and places them in descending order to form a three-digit number. Silvia independently does the same with three distinct digits from $\{1,2,\ldots,8\}$. What is the probability that Bernardo's number is larger?
  1. $\frac{47}{72}$
  2. $\frac{37}{56}$
  3. $\frac23$
  4. $\frac{49}{72}$
  5. $\frac{39}{56}$