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=532&top_left_y=997&width=532&height=212&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f69f","slug":"number-of-positive-integral-solution-of-x-y-z-6-is","content":"Number of positive integral solution of x + y + z = 6 is","options":[{"_id":"68a37f397f15af4716b691c3","text":"4 !","sequence":0,"isCorrect":false},{"_id":"68a37f397f15af4716b691c4","text":"3 !","sequence":1,"isCorrect":false},{"_id":"68a37f397f15af4716b691c5","text":"6!","sequence":2,"isCorrect":false},{"_id":"68a37f397f15af4716b691c6","text":"10","sequence":3,"isCorrect":true}],"correct_answer":"10","explanation":"Number of positive integral solution of x+y+z = n is\n\nCoefficient of xⁿ in (x+x² + x³ + ...)³ = Coefficient of xⁿ (1+x+x² + ...)³\n\n= Coefficient of x^n-3 in \\(\\left( \\frac{1}{1 - x} \\right)^{3}\\)\n\n= Coefficient of x^n-3 in (1-x)^-3 = \\(n - 1C_{n - 3} =^{n - 1}C_{2}\\)\n\nHere n = 6\n\n∴ Required solution = \\(5C_{2} = 10\\)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.755Z","__v":0,"vector_store_id":"d63ca2f1-fdb9-4ef4-810d-e5495e022d25","updated_at":"2024-08-30T21:49:38.755Z","isStarred":false},"params":{"questionSlug":"number-of-positive-integral-solution-of-x-y-z-6-is"}}]}]]

Question: Number of positive integral solution of x + y + z = 6 is...

Solution