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

  • question_answer
    The number of ways in which a committee  of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains at least 3 ladies is [Kerala (Engg.) 2002]

    A) 252

    B) 672

    C) 444

    D) 420

    Correct Answer: A

    Solution :

    There can be two types of committees (i) Containing 3 men and 3 ladies (ii) Containing 2 men and 4 ladies \ Required number of ways = \[{{(}^{8}}{{C}_{3}}\,\times {{\,}^{4}}{{C}_{3}})\,+\,{{(}^{8}}{{C}_{2}}\,\times {{\,}^{4}}{{C}_{4}})=252\].


You need to login to perform this action.
You will be redirected in 3 sec spinner