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A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of chooses available to him.
Total number questions = 13Total number questions to be answered = 10It is given that he must choose at least 4 from the first five questions.Case 1: He answered 4 from the first 5 questions and 6 from the remaining 8.Number of chooses \( = {5_{{C_4}}} \times {8_{{C_6}}} = 140\)Case 2: He answered 5 from the first 5 questions and 5 from the remaining 8.Number of chooses \( = {5_{{C_5}}} \times {8_{{C_3}}} = 56\)Total number of chooses = 140 + 56 = 196
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