{"status": "success", "data": {"description_md": "Six ants simultaneously stand on the six vertices of a regular octahedron, with each ant at a different vertex. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. What is the probability that no two ants arrive at the same vertex?\n\n$\\mathrm{(A)}\\ \\frac {5}{256}\\qquad\\mathrm{(B)}\\ \\frac {21}{1024}\\qquad\\mathrm{(C)}\\ \\frac {11}{512}\\qquad\\mathrm{(D)}\\ \\frac {23}{1024}\\qquad\\mathrm{(E)}\\ \\frac {3}{128}$\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>Six ants simultaneously stand on the six vertices of a regular octahedron, with each ant at a different vertex. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. What is the probability that no two ants arrive at the same vertex?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac {5}{256}\\qquad\\mathrm{(B)}\\ \\frac {21}{1024}\\qquad\\mathrm{(C)}\\ \\frac {11}{512}\\qquad\\mathrm{(D)}\\ \\frac {23}{1024}\\qquad\\mathrm{(E)}\\ \\frac {3}{128}</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": 5, "problem_name": "2005 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/05_amc12B_p24"}}