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 made out of the letters of the word MOBILE when consonants always occupy odd places is [RPET 1999]

    A) 20

    B) 36

    C) 30

    D) 720

    Correct Answer: B

    Solution :

      The word MOBILE has three even places and three odd places. It has 3 consonants and 3 vowels.  In three odd places we have to fix up 3 consonants which can be done in \[{}^{3}{{P}_{3}}\] ways. Now, remaining three places we have to fix up remaining three places we have to fix up remaining three which can be done in \[{}^{3}{{P}_{3}}\] ways. The total number of ways \[={}^{3}{{P}_{3}}\times {}^{3}{{P}_{3}}\]= 36.


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