{"id":"aqua_rat:ad816c2b1d02b712f0121bedb50a4c29","source_id":"aqua_rat","source_item_id":"ad816c2b1d02b712f0121bedb50a4c29","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"In how many ways to choose a group of 3 people from 6 couples so that no couple is chosen","stimulus":"","stimulus_html":null,"stem_html":"<p>In how many ways to choose a group of 3 people from 6 couples so that no couple is chosen</p>","rationale_html":"<p>Number of ways 3 people can be chosen from 12 = 12C3 = 220</p><p>Number of ways a couple can be chosen = 6</p><p>Number of ways the third person can be chosen = 10C1 = 10</p><p>Hence, total number of ways a couple with another person can be chosen = 6*10 = 60</p><p>Therefore, total number of ways a couple cannot be chosen = 220-60 = 160</p><p>D</p>","correct_answer":["D"],"equiv_key":"b95980a138724b51192c9b43","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>60</p>","ord":0},{"label":"B","content_html":"<p>120</p>","ord":1},{"label":"C","content_html":"<p>140</p>","ord":2},{"label":"D","content_html":"<p>160</p>","ord":3},{"label":"E","content_html":"<p>180</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}