{"status": "success", "data": {"description_md": "Two subsets of the set $S=\\lbrace a,b,c,d,e\\rbrace$ are to be chosen so that their union is $S$ and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?\n\n$\\mathrm{(A)}\\ 20\\qquad\\mathrm{(B)}\\ 40\\qquad\\mathrm{(C)}\\ 60\\qquad\\mathrm{(D)}\\ 160\\qquad\\mathrm{(E)}\\ 320$", "description_html": "<p>Two subsets of the set  <span class=\"katex--inline\">S=\\lbrace a,b,c,d,e\\rbrace</span>  are to be chosen so that their union is  <span class=\"katex--inline\">S</span>  and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 20\\qquad\\mathrm{(B)}\\ 40\\qquad\\mathrm{(C)}\\ 60\\qquad\\mathrm{(D)}\\ 160\\qquad\\mathrm{(E)}\\ 320</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": "2008 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p24", "prev": "/problem/08_amc10A_p22"}}