{"status": "success", "data": {"description_md": "Let $n=\\dfrac{(2^{11})!}{(2^6)!}$ and let $k$ be a randomly chosen positive factor of $n$. The probability that $k$ is even can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a+b$.", "description_html": "<p>Let <span class=\"katex--inline\">n=\\dfrac{(2^{11})!}{(2^6)!}</span> and let <span class=\"katex--inline\">k</span> be a randomly chosen positive factor of <span class=\"katex--inline\">n</span>. The probability that <span class=\"katex--inline\">k</span> is even can be expressed as <span class=\"katex--inline\">\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime positive integers. Compute <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p16", "prev": "/problem/txo2024team-p14"}}