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

  • question_answer
    A total number of words which can be formed out of the letters \[a,\ b,\ c,\ d,\ e,\ f\] taken 3 together such that each word contains at least one vowel, is

    A) 72

    B) 48

    C) 96

    D) None of these

    Correct Answer: C

    Solution :

    The required number of words is \[{{(}^{2}}{{C}_{1}}{{\times }^{4}}{{C}_{2}}{{+}^{2}}{{C}_{2}}{{\times }^{4}}{{C}_{1}})3\ !\ =96\].


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