Question
Determine the number of unique arrangements of the
letters in “ELEPHANT” if the vowels always stay together.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! × 3!/2! = 720 × 3 = 2160
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