{"status": "success", "data": {"description_md": "Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those girls but disliked by the third. In how many different ways is this possible?\n\n$\\textbf{(A)}\\ 108\\qquad\\textbf{(B)}\\ 132\\qquad\\textbf{(C)}\\ 671\\qquad\\textbf{(D)}\\ 846\\qquad\\textbf{(E)}\\ 1105$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those girls but disliked by the third. In how many different ways is this possible?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 108\\qquad\\textbf{(B)}\\ 132\\qquad\\textbf{(C)}\\ 671\\qquad\\textbf{(D)}\\ 846\\qquad\\textbf{(E)}\\ 1105</span> </p>&#10;<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": "2012 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12B_p17", "prev": "/problem/12_amc12B_p15"}}