{"status": "success", "data": {"description_md": "Three distinct vertices of a cube are chosen at random. What is the probability that the plane determined by these three vertices contains points inside the cube?\n\n$\\mathrm{(A)}\\ \\frac{1}{4}\n\\qquad\n\\mathrm{(B)}\\ \\frac{3}{8}\n\\qquad\n\\mathrm{(C)}\\ \\frac{4}{7}\n\\qquad\n\\mathrm{(D)}\\ \\frac{5}{7}\n\\qquad\n\\mathrm{(E)}\\ \\frac{3}{4}$", "description_html": "<p>Three distinct vertices of a cube are chosen at random. What is the probability that the plane determined by these three vertices contains points inside the cube?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{1}{4}\n\\qquad\n\\mathrm{(B)}\\ \\frac{3}{8}\n\\qquad\n\\mathrm{(C)}\\ \\frac{4}{7}\n\\qquad\n\\mathrm{(D)}\\ \\frac{5}{7}\n\\qquad\n\\mathrm{(E)}\\ \\frac{3}{4}</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": 4, "problem_name": "2009 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p25", "prev": "/problem/09_amc10A_p23"}}