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There are three sections in a question paper, each containing 5 questions. A candidate has to solve any 5 questions, choosing at least one from each section. Find the number of ways in which the candidate can choose the questions.A. `""^(15)C_(5)`B. `""^(3)C_(1)xx""^(12)C_(4)`C. 2250D. 2253 |
Answer» We observe that Total number of ways of choosing at least one question from each section = Total number of ways of choosing 5 questions out of 15 questions - Number of ways of selecting 5 questions from 2 sections only - Number of ways of choosing 5 questions from one section only. `=""^(15)C_(5)-""^(3)C_(2)(""^10C_(5)-""^(2)C_(1)xx""^(5)C_(5))-""^(3)C_(1)xx""^(5)C_(5)` `=""^(15)C_(5)-3xx""^(10)C_(5)+6-3=2250` |
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