There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways in which the candidate can choose the questions, is:
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Official solution
\[ \therefore \] Total number of selection of 5 questions
= \[\left( {{}^5{C_1}.{}^5{C_2}.{}^5{C_2}} \right)\] ×3 +\left( {{}^5{C_1}.{}^5{C_1}.{}^5{C_3}} \right) ( \] \times 3
= 5×10×10×3 + 5×5×10×