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

  • question_answer
    Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done if the group is to have a majority of boys [MP PET 1994]

    A) 120

    B) 90

    C) 100

    D) 80

    Correct Answer: C

    Solution :

    1 girl and 6 boys \[{{=}^{4}}{{C}_{1}}{{\times }^{6}}{{C}_{6}}=4\] 2 girls and 5 boys \[{{=}^{4}}{{C}_{2}}{{\times }^{6}}{{C}_{5}}=36\] 3 girls and 4 boys \[{{=}^{4}}{{C}_{3}}{{\times }^{6}}{{C}_{4}}=60\] Hence total ways\[60+36+4=100\].


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