st","extracted_subject":"MATH","extracted_chapter":"PERMUTATIONS AND COMBINATIONS","extracted_topic":"DEFINITON OF COMBINATIONS, CONDITION COMBINATIONS, DIVISION INTO GROUPS, DERANGEMENTS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2013.png?top_left_x=0&top_left_y=515&width=532&height=217&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f69a","slug":"if-supnsupcsub4sub-210-then-sup12supcsubnsub","content":"If ⁿC₄ = 210, then ¹²C_n.","options":[{"_id":"68a3fd7e7f15af4716c87588","text":"33","sequence":0,"isCorrect":false},{"_id":"68a3fd7e7f15af4716c87589","text":"22","sequence":1,"isCorrect":false},{"_id":"68a3fd7e7f15af4716c8758a","text":"11","sequence":2,"isCorrect":false},{"_id":"68a3fd7e7f15af4716c8758b","text":"66","sequence":3,"isCorrect":true}],"correct_answer":"66","explanation":"\\[\\frac{\\mathbf{n(n}\\mathbf{-}\\mathbf{1)(n}\\mathbf{-}\\mathbf{2)(n}\\mathbf{-}\\mathbf{3)}}{\\mathbf{24}}\\mathbf{= 210.}\\]\n\nn(n - 1) (n - 2) (n - 3) = 210 x 24 = 7 x 3 x 5 x 2 x 4 x 3 x 2\n\n= 7 x 8 x 9 x 10.\n\nn = 10.\n\n¹²C_n = ¹²C₁₀ = ¹²C₂ = \\(\\frac{12x11}{2}\\) = 66.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.754Z","__v":0,"vector_store_id":"20d3c4a7-f707-4ffc-9adf-a684d0bc24bf","updated_at":"2024-08-30T21:49:38.754Z","isStarred":false},"params":{"questionSlug":"if-supnsupcsub4sub-210-then-sup12supcsubnsub"}}]}]]

Question: If <sup>n</sup>C<sub>4</sub> = 210, then <sup>12</sup>C<sub>n</sub>....

Solution