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    Question

    In how many ways can the letters of the word

    ‘EDUCATION’ be arranged such that the vowels take the odd positions?
    A 2880 Correct Answer Incorrect Answer
    B 2400 Correct Answer Incorrect Answer
    C 2160 Correct Answer Incorrect Answer
    D 2520 Correct Answer Incorrect Answer

    Solution

    According to the question,
    There are 5 odd positions and 5 vowels, all distinct: E, U, A, I, O
    Therefore, number of ways of arranging the 5 vowels in odd positions = 5! = 120 ways
    The remaining 4 consonants (D, C, T, N) can be arranged in the even positions = 4! = 24 ways
    Required number of ways = 120 × 24 = 2880

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