JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • 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 [Kerala (Engg.) 2005]

    A) 140

    B) 196

    C) 280

    D) 346

    E) 265

    Correct Answer: A

    Solution :

     Number of ways for select 4 Questions out of 5 Questions. Number of ways \[=\,{{\,}^{5}}{{C}_{4}}=5\] Remaining Questions =8 Remaining Questions for solving =6 \ Number of ways \[{{\,}^{8}}{{C}_{6}}=28\] Number of total ways \[{{=}^{5}}{{C}_{4}}\times {{\,}^{8}}{{C}_{6}}\]\[=5\times 28\]\[=140\].


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