test","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_2022.png?top_left_x=0&top_left_y=1399&width=532&height=270&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f839","slug":"there-are-13-players-of-cricket-out-of-which-4-are","content":"There are 13 players of cricket out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?","options":[{"_id":"68a3b2347f15af4716bf593b","text":"72","sequence":0,"isCorrect":false},{"_id":"68a3b2347f15af4716bf593c","text":"78","sequence":1,"isCorrect":true},{"_id":"68a3b2347f15af4716bf593d","text":"42","sequence":2,"isCorrect":false},{"_id":"68a3b2347f15af4716bf593e","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"78","explanation":"Team of eleven may be selected\n\n(i) 2 bowlers + 9 others\n\n(ii) 3 bowlers + 8 others\n\n(iii) 4 bowlers + 7 others\n\n= (⁴C₂ × ⁹C₉) + (⁴C₃ × ⁹C₈) + (⁴C₄ × ⁹C₇) ̃ 78","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.859Z","__v":0,"vector_store_id":"b9e3f540-4ff4-4cd5-919b-1449d7720992","updated_at":"2024-08-30T21:49:38.859Z","isStarred":false},"params":{"questionSlug":"there-are-13-players-of-cricket-out-of-which-4-are"}}]}]]

Question: There are 13 players of cricket out of which 4 are bowlers. In how many ways a team of eleven be sel...

Solution