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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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