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 question. The number of choices available to him is [AIEEE 2003]

    A) 140

    B) 196

    C) 280

    D) 346

    Correct Answer: B

    Solution :

    As for given question two cases are possible. (i) Selecting 4 out of first 5 questions and 6 out of remaining 8 questions \[={{\,}^{5}}{{C}_{4}}\,\times {{\,}^{8}}{{C}_{6}}=140\] choices. (ii) Selecting 5 out of first 5 questions and 5 out of remaining 8 questions \[={{\,}^{5}}{{C}_{5}}\,\times {{\,}^{8}}{{C}_{5}}=56\] choices. \ Total no. of choices = 140 + 56 = 196.


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