{"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$\\mathrm{(A)}\\ \\frac{1}{2}\\qquad\\mathrm{(B)}\\ \\frac{3}{5}\\qquad\\mathrm{(C)}\\ \\frac{2}{3}\\qquad\\mathrm{(D)}\\ \\frac{4}{5}\\qquad\\mathrm{(E)}\\ 1$", "description_html": "<p>Six distinct positive integers are randomly chosen between <span class=\"katex--inline\">1</span> and <span class=\"katex--inline\">2006</span>, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of <span class=\"katex--inline\">5</span>?</p>&#10;<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>&#10;", "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"}}