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2011 AMC 10A Problem 21

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2011 AMC 10A Problem 21AMC 10 Step by Step
Name:                             Date: September 13, 2026
Conditional Probability & States · difficulty 4 of 5 · about 6 min · position P21-25

Two counterfeit coins of equal weight are mixed with 8 identical genuine coins. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. A pair of coins is selected at random without replacement from the 10 coins. A second pair is selected at random without replacement from the remaining 8 coins. The combined weight of the first pair is equal to the combined weight of the second pair. What is the probability that all 4 selected coins are genuine?

  1. A)

    711\frac{7}{11}

  2. B)

    913\frac{9}{13}

  3. C)

    1115\frac{11}{15}

  4. D)

    1519\frac{15}{19}

  5. E)

    1516\frac{15}{16}

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