Multiple choice

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

  1. 360

  2. 480

  3. 720

  4. 5040

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

The word LEADING has 7 letters, including 3 vowels (E, A, I) and 4 consonants (L, D, N, G). Treating the vowels as a single unit, we have 5 items to arrange (the vowel block + 4 consonants), which is 5! ways, and the 3 vowels can be arranged among themselves in 3! ways. Total arrangements = 5! * 3! = 120 * 6 = 720.

AI explanation

The word LEADING has 7 letters with 3 vowels (E, A, I) and 4 consonants. When the 3 vowels are treated as a single unit, there are 5 units to arrange (4 consonants plus 1 vowel unit), which can be done in 5! ways, or 120 ways. The 3 vowels can be arranged within their unit in 3! ways, which is 6 ways. Multiplying 120 by 6 gives 720.

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