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Math Help - combination

  1. #1
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    combination

    "A question paper is divided into two groups, each containing 5 questions. A candidate is required to solve 6 questions in all but he is not permitted to attempt more than 4 questions from each group. Find the number of ways in which the candidate can select the question."


    I thought he could either choose 3 from each group, or choose 4 from one group and 2 from the other. (5C3)(5C3)+(5C4)(5C2)=150 but the answer is supposed to be 200. I thought of multiplying 150 by 2 because choosing three from group 1 and three from group 2 is distinct from doing it the other way around. But that's 300, and the answer is supposed to be 200. Please assist.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Pewł View Post
    "A question paper is divided into two groups, each containing 5 questions. A candidate is required to solve 6 questions in all but he is not permitted to attempt more than 4 questions from each group. Find the number of ways in which the candidate can select the question."


    I thought he could either choose 3 from each group, or choose 4 from one group and 2 from the other. (5C3)(5C3)+(5C4)(5C2)=150 but the answer is supposed to be 200. I thought of multiplying 150 by 2 because choosing three from group 1 and three from group 2 is distinct from doing it the other way around. But that's 300, and the answer is supposed to be 200. Please assist.
    The number of choices is {5\choose 4}{5\choose2}+{5\choose 3}{5\choose 3}+{5\choose 2}{5\choose 4}=200 since you can choose:

    4 Q's from Group 1 and 2 Q's from Group 2 OR
    3 Q's from Group 1 and 3 Q's from Group 2 OR
    2 Q's from Group 1 and 4 Q's from Group 2
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