{"status": "success", "data": {"description_md": "**POTD July 7, 2024**\n\n$5$ students, all with distinct ages, are randomly seated in a row at the movies. The probability that, from left to right, no three consecutive students are seated in increasing age order is $\\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.", "description_html": "<p><strong>POTD July 7, 2024</strong></p>&#10;<p><span class=\"katex--inline\">5</span> students, all with distinct ages, are randomly seated in a row at the movies. The probability that, from left to right, no three consecutive students are seated in increasing age order is <span class=\"katex--inline\">\\frac{m}{n}</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #210", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}