{"status": "success", "data": {"description_md": "Two subsets of the set $\\mathcal{S}=\\lbrace a,b,c,d,e\\rbrace$ are to be chosen so that their union is $\\mathcal{S}$ 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\">\\mathcal{S}=\\lbrace a,b,c,d,e\\rbrace</span> are to be chosen so that their union is <span class=\"katex--inline\">\\mathcal{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>&#10;<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>&#10;", "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"}}