st","extracted_subject":"MATH","extracted_chapter":"BINOMIAL THEOREM AND MATHEMATICAL INDUCTION","extracted_topic":"BINOMIAL THEOREM FOR ANY INDEX","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1986.png?top_left_x=532&top_left_y=1774&width=532&height=227&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f295","slug":"the-value-of-sup47supcsub4sub-sum_r-1552---rc_3","content":"The value of ⁴⁷C₄ + \$\\sum_{r = 1}^{5}{(52 - r)C_{3}}\$","options":[{"_id":"68a971cc7f15af4716d5ed8e","text":"\$53C_{3}\$","sequence":0,"isCorrect":false},{"_id":"68a971cc7f15af4716d5ed8f","text":"\$52C_{4}\$","sequence":1,"isCorrect":true},{"_id":"68a971cc7f15af4716d5ed90","text":"\$52C_{5}\$","sequence":2,"isCorrect":false},{"_id":"68a971cc7f15af4716d5ed91","text":"None","sequence":3,"isCorrect":false}],"correct_answer":"$$52C_{4}$","explanation":"⁴⁷C₄ + \$\\sum_{r = 1}^{5}{(52 - r)C_{3}}\$\n\n\\[\\Rightarrow \\underset{}{\\overset{47C_{4} +^{51}C_{3} +^{50}C_{3} +^{49}C_{3} +^{48}C_{3} +^{47}C_{3}}{︸}}\\]\n\n\$48C_{4}\$\n\n\\[\\Rightarrow \\underset{}{\\overset{48C_{4} +^{51}C_{3} +^{50}C_{3} +^{49}C_{3} +^{48}C_{3}}{︸}}\\]\n\n\$49C_{4}\$\n\nSimilarly proceeding we get ⁵²C₄.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.505Z","__v":0,"vector_store_id":"9cfbbdea-39be-4ce4-8581-7b07eb41740f","updated_at":"2024-08-30T21:49:38.505Z","isStarred":false},"params":{"questionSlug":"the-value-of-sup47supcsub4sub-sum_r-1552---rc_3"}}]}]]

Question: The value of <sup>47</sup>C<sub>4</sub> + \(\sum_{r = 1}^{5}{(52 - r)C_{3}}\)...

Solution