{"id":"aqua_rat:69d98869b46d3f3ad890d82e09537ce6","source_id":"aqua_rat","source_item_id":"69d98869b46d3f3ad890d82e09537ce6","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 can the letters of the word \"PROBLEC\" be rearranged to make 7 letter words such that none of the letters repeat?","stimulus":"","stimulus_html":null,"stem_html":"<p>In how many ways can the letters of the word &quot;PROBLEC&quot; be rearranged to make 7 letter words such that none of the letters repeat?</p>","rationale_html":"<p>There are seven positions to be filled.</p><p>The first position can be filled using any of the 7 letters contained in PROBLEM.</p><p>The second position can be filled by the remaining 6 letters as the letters should not repeat.</p><p>The third position can be filled by the remaining 5 letters only and so on.</p><p>758</p><p>Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! Ways.</p><p>C</p>","correct_answer":["C"],"equiv_key":"9db12d182f414ef8970f9f34","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>2!</p>","ord":0},{"label":"B","content_html":"<p>3!</p>","ord":1},{"label":"C","content_html":"<p>7!</p>","ord":2},{"label":"D","content_html":"<p>8!</p>","ord":3},{"label":"E","content_html":"<p>9!</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":[]}