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2010 AMC 10A Problem 18

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2010 AMC 10A Problem 18AMC 10 Step by Step
Name:                             Date: September 13, 2026
Basic Probability · difficulty 4 of 5 · about 6 min · position P16-20

Bernardo randomly picks 3 distinct numbers from the set {1,2,3,4,5,6,7,8,9}\{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}\{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. A)

    4772\frac{47}{72}

  2. B)

    3756\frac{37}{56}

  3. C)

    23\frac{2}{3}

  4. D)

    4972\frac{49}{72}

  5. E)

    3956\frac{39}{56}

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