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Bernardo and Silvia counts from sets

Source: AMC 12A 2010, Problem 16

February 10, 2010
probabilityAMC

Problem Statement

Bernardo randomly picks 3 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 3-digit number. Silvia randomly picks 3 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 3-digit number. What is the probability that Bernardo's number is larger than Silvia's number? <spanclass=′latex−bold′>(A)</span> 4772<spanclass=′latex−bold′>(B)</span> 3756<spanclass=′latex−bold′>(C)</span> 23<spanclass=′latex−bold′>(D)</span> 4972<spanclass=′latex−bold′>(E)</span> 3956 <span class='latex-bold'>(A)</span>\ \frac {47}{72}\qquad <span class='latex-bold'>(B)</span>\ \frac {37}{56}\qquad <span class='latex-bold'>(C)</span>\ \frac {2}{3}\qquad <span class='latex-bold'>(D)</span>\ \frac {49}{72}\qquad <span class='latex-bold'>(E)</span>\ \frac {39}{56}
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