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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    The number of different words which can be formed from the letters of the word LUCKNOW when the vowels always occupy even places in

    A) 120

    B) 720

    C) 400

    D) None of these

    Correct Answer: B

    Solution :

    [b] In LUCKNOW, number of letters = 7 (all distinct), vowels (U, O) =2, consonants (L, C, K, N, W)=5 There are 7 letters so 7 places are required. Number of even places are 3 and vowels are 2, so 2 vowels can be placed in \[^{3}{{C}_{2}}.2!=6\] and 5 consonants can be placed in remaining places in 5! Ways. Hence, number of words \[=6.5!=720.\]


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