Multiple choice

In how many different ways can the letters of the word ‘DICTIONARY’ be arranged in such a way that the vowels always come together?

  1. 15120

  2. 10960

  3. 60480

  4. 30240

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

DICTIONARY has 10 letters. Vowels: I, I, O, A, Y (5 vowels). Treat the 5 vowels as one unit. We have 6 units to arrange (5 consonants + 1 vowel group). 6! ways = 720. The 5 vowels within their group can be arranged in 5! ways = 120. Total arrangements = 720 × 120 = 86400. However, standard approach counts only I, I, O, A as vowels (4 vowels): 7 units × 4!/2! (since I repeats) = 5040 × 12 = 60480.

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