{"status": "success", "data": {"description_md": "Bernardo randomly picks 3 distinct numbers from the set $\\{1,2,3,4,5,6,7,8,9\\}$ and arranges them in descending order to form a 3-digit number. Silvia randomly picks 3 distinct numbers from the set $\\{1,2,3,4,5,6,7,8\\}$ 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$\\textbf{(A)}\\ \\frac{47}{72} \\qquad \\textbf{(B)}\\ \\frac{37}{56} \\qquad \\textbf{(C)}\\ \\frac{2}{3} \\qquad \\textbf{(D)}\\ \\frac{49}{72} \\qquad \\textbf{(E)}\\ \\frac{39}{56}$", "description_html": "<p>Bernardo randomly picks 3 distinct numbers from the set  <span class=\"katex--inline\">\\{1,2,3,4,5,6,7,8,9\\}</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\">\\{1,2,3,4,5,6,7,8\\}</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>\n<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>\n<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 10A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc10A_p19", "prev": "/problem/10_amc10A_p17"}}