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

  • question_answer
    All the letters of the word ?EAMCET? are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is [EAMCET 1987; DEC 2000]

    A) 360

    B) 114

    C) 72

    D) 54

    Correct Answer: C

    Solution :

    First, we arrange 3 consonants in \[3\ !\] ways and then at four places (two places between them and two places on two sides) 3 vowels can be placed in \[^{4}{{P}_{3}}\times \frac{1}{2\ !}\] ways. Hence the required number\[=3\ !\ {{\times }^{4}}{{P}_{3}}\times \frac{1}{2\ !}=72\].


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