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 that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is [Karnataka CET  2003]

    A) 36

    B) 574

    C) 144

    D) 754

    Correct Answer: C

    Solution :

    Out of 7 places, 4 places are odd and 3 even. Therefore 3 vowels can be arranged in 3 even places in \[^{3}{{P}_{3}}\] ways and remaining 4 consonants can be arranged in 4 odd places in \[^{4}{{P}_{4}}\] ways. Hence required no. of ways = \[^{3}{{P}_{3}}\] × \[^{4}{{P}_{4}}\] = 144.

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