Multiple choice

In how many different ways can the letters of the word (DETAIL) be arranged in such a way that vowels may occupy only odd positions?

  1. 18

  2. 720

  3. 36

  4. 320

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word DETAIL has 6 letters with 2 vowels (E, A, I) and 3 consonants (D, T, L). Odd positions are 1, 3, 5 - we choose 3 of these for vowels: 3P3 = 6 ways. Even positions 2, 4, 6 get consonants: 3P3 = 6 ways. Total = 6 × 6 = 36 arrangements. The vowels must occupy odd positions, not all odd positions.

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