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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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