JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, he is not permitted to attempt more than 4 questions from either group. The number of different ways in which the candidate can choose 6 questions is

    A) 50                    

    B) 150

    C) 200     

    D) 250

    Correct Answer: C

    Solution :

    [c] The number of ways the candidate can choose questions under the given conditions is enumerated below.
    Group 1 Group 2 Number of ways
    4 2 \[{{(}^{5}}{{C}_{4}}){{(}^{5}}{{C}_{2}})=50\]
    3 3 \[{{(}^{5}}{{C}_{3}}){{(}^{5}}{{C}_{3}})=100\]
    2 4 \[{{(}^{5}}{{C}_{2}}){{(}^{5}}{{C}_{4}})=50\]
      Total number of ways 200

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