{"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 <span class=\"katex--inline\">3</span> 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 <span class=\"katex--inline\">3</span>-digit number. Silvia randomly picks <span class=\"katex--inline\">3</span> 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 <span class=\"katex--inline\">3</span>-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;", "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"}}