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      Question

      Determine the number of unique arrangements of the

      letters in “ELEPHANT” if the vowels always stay together.
      A 1625 Correct Answer Incorrect Answer
      B 2820 Correct Answer Incorrect Answer
      C 2160 Correct Answer Incorrect Answer
      D 1750 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      The word “ELEPHANT” has 8 letters.

      Vowels: E, E, A → 3 vowels (E repeated twice)

      Consonants: L, P, H, N, T → 5 consonants

      Treat all vowels as one block → total entities to arrange: 1 vowel block + 5 consonants = 6

      So, outer arrangement = 6!

      Inside the vowel block (E, E, A) → 3 letters with 2 E’s repeated → internal arrangement = 3!/2!

      Total number of words = 6! Ă— 3!/2! = 720 Ă— 3 = 2160

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