{"status": "success", "data": {"description_md": "Let $S$ be the set of permutations of the sequence $1,2,3,4,5$ for which the first term is not $1$. A permutation is chosen randomly from $S$. The probability that the second term is $2$, in lowest terms, is $a/b$. What is $a+b$?\n\n$\\mathrm{(A)}\\ 5\\qquad\\mathrm{(B)}\\ 6\\qquad\\mathrm{(C)}\\ 11\\qquad\\mathrm{(D)}\\ 16\\qquad\\mathrm{(E)}\\ 19$\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>Let <span class=\"katex--inline\">S</span> be the set of permutations of the sequence <span class=\"katex--inline\">1,2,3,4,5</span> for which the first term is not <span class=\"katex--inline\">1</span>. A permutation is chosen randomly from <span class=\"katex--inline\">S</span>. The probability that the second term is <span class=\"katex--inline\">2</span>, in lowest terms, is <span class=\"katex--inline\">a/b</span>. What is <span class=\"katex--inline\">a+b</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 5\\qquad\\mathrm{(B)}\\ 6\\qquad\\mathrm{(C)}\\ 11\\qquad\\mathrm{(D)}\\ 16\\qquad\\mathrm{(E)}\\ 19</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p20", "prev": "/problem/03_amc12B_p18"}}