{"status": "success", "data": {"description_md": "There are $10$ people standing equally spaced around a circle. Each person knows exactly $3$ of the other $9$ people: the $2$ people standing next to her or him, as well as the person directly across the circle. How many ways are there for the $10$ people to split up into $5$ pairs so that the members of each pair know each other?\n\n$\\textbf{(A)}\\ 11 \\qquad\\textbf{(B)}\\ 12 \\qquad\\textbf{(C)}\\  13 \\qquad\\textbf{(D)}\\ 14 \\qquad\\textbf{(E)}\\ 15$", "description_html": "<p>There are  <span class=\"katex--inline\">10</span>  people standing equally spaced around a circle. Each person knows exactly  <span class=\"katex--inline\">3</span>  of the other  <span class=\"katex--inline\">9</span>  people: the  <span class=\"katex--inline\">2</span>  people standing next to her or him, as well as the person directly across the circle. How many ways are there for the  <span class=\"katex--inline\">10</span>  people to split up into  <span class=\"katex--inline\">5</span>  pairs so that the members of each pair know each other?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 11 \\qquad\\textbf{(B)}\\ 12 \\qquad\\textbf{(C)}\\  13 \\qquad\\textbf{(D)}\\ 14 \\qquad\\textbf{(E)}\\ 15</span> </p>\n<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": "2020 AMC 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10B_p18", "prev": "/problem/20_amc10B_p16"}}