{"status": "success", "data": {"description_md": "Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5? \n \n\n$\\mathrm{(A)}\\ \\frac{1}{2}\\qquad\\mathrm{(B)}\\ \\frac{3}{5}\\qquad\\mathrm{(C)}\\ \\frac{2}{3}\\qquad\\mathrm{(D)}\\ \\frac{4}{5}\\qquad\\mathrm{(E)}\\ 1$", "description_html": "<p>Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{1}{2}\\qquad\\mathrm{(B)}\\ \\frac{3}{5}\\qquad\\mathrm{(C)}\\ \\frac{2}{3}\\qquad\\mathrm{(D)}\\ \\frac{4}{5}\\qquad\\mathrm{(E)}\\ 1</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": "2006 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10A_p21", "prev": "/problem/06_amc10A_p19"}}