{"status": "success", "data": {"description_md": "Let $S$ be the [[set]] of [[permutation]]s 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$\\mathrm{(A)}\\ 5<br>\\qquad\\mathrm{(B)}\\ 6<br>\\qquad\\mathrm{(C)}\\ 11<br>\\qquad\\mathrm{(D)}\\ 16<br>\\qquad\\mathrm{(E)}\\ 19$\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 [[permutation]]s 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><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": "2003 AMC 12B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p20", "prev": "/problem/03_amc12B_p18"}}