Multiple choice

In how many different ways can the letters of the word $'LEADING'$ be arranged so that all the vowels are together?

  1. $360$
  2. $480$
  3. $720$
  4. $5040$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word LEADING has 7 letters: L, E, A, D, I, N, G. The vowels are E, A, I. Treating (EAI) as one unit, we have 5 units: {L, D, N, G, (EAI)}. These can be arranged in 5! = 120 ways. The vowels themselves can be arranged in 3! = 6 ways. Total = 120 * 6 = 720.

AI explanation

The word LEADING has 6 total letters and 3 vowels (E, A, I). Using the method of grouping, we treat the 3 vowels as a single unit, giving us 4 units to arrange (the vowel unit plus L, D, N, G). The number of arrangements for these 4 units is 4 factorial, which is 24. The 3 vowels can be arranged within their unit in 3 factorial ways, which is 6. Multiplying these gives 24 multiplied by 6, resulting in 720 ways.

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