JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is

    A) 4!

    B) \[3\,!\,\,\times \,\,4\,!\]

    C) 7 !

    D) None of these

    Correct Answer: A

    Solution :

    \[\bullet \ A\bullet I\bullet U\bullet \] The pointed places to be filled by\[MXMM\]. Hence required number of ways \[3\ !\ \times \frac{4\ !}{3\ !}=4\ !\] {Since three vowels can be arranged in \[3\ !\] ways also}.

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