Multiple choice

How many different words can be formed using all the letters of the word $'ALLAHABAD' $ when all the vowels are together?

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

The word ALLAHABAD has 9 letters: A, A, A, A, L, L, H, B, D. The vowels are A, A, A, A. Treating the four A's as a single block, we arrange the block and the remaining letters (L, L, H, B, D). There are 6 items to arrange: (AAAA), L, L, H, B, D. The number of arrangements is 6! / 2! (for the two L's) = 720 / 2 = 360.

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