JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    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 choices available to him is

    A) 346

    B) 140

    C) 196

    D) 280

    Correct Answer: C

    Solution :

    [c] As for given question two cases are possible. (i) Selecting 5 out of first five question and 6 out of remaining 5 question \[{{=}^{5}}{{C}_{4}}{{\times }^{8}}{{C}_{6}}=140\] choices. (ii) Selecting 5 out of first five question and 5 out of remaining 8 questions \[{{=}^{5}}{{C}_{5}}{{\times }^{8}}{{C}_{5}}=56\] choices. Therefore, total number of choices \[=140+56=196.\]


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