{"status": "success", "data": {"description_md": "Bernardo randomly picks 3 distinct numbers from the set $\\{1,2,3,...,7,8,9\\}$ and arranges them in descending order to form a 3-digit number. Silvia randomly picks 3 distinct numbers from the set $\\{1,2,3,...,6,7,8\\}$ 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?\n\n$\\textbf{(A)}\\ \\frac{47}{72} \\qquad \\textbf{(B)}\\ \\frac{37}{56} \\qquad \\textbf{(C)}\\ \\frac{2}{3} \\qquad \\textbf{(D)}\\ \\frac{49}{72} \\qquad \\textbf{(E)}\\ \\frac{39}{56}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Bernardo randomly picks 3 distinct numbers from the set  <span class=\"katex--inline\">\\{1,2,3,...,7,8,9\\}</span>  and arranges them in descending order to form a 3-digit number. Silvia randomly picks 3 distinct numbers from the set  <span class=\"katex--inline\">\\{1,2,3,...,6,7,8\\}</span>  and also arranges them in descending order to form a 3-digit number. What is the probability that Bernardo&#8217;s number is larger than Silvia&#8217;s number?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{47}{72} \\qquad \\textbf{(B)}\\ \\frac{37}{56} \\qquad \\textbf{(C)}\\ \\frac{2}{3} \\qquad \\textbf{(D)}\\ \\frac{49}{72} \\qquad \\textbf{(E)}\\ \\frac{39}{56}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2010 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p17", "prev": "/problem/10_amc12A_p15"}}