Question
How many arrangements of the word COMMITTEE are
possible if the vowels are always together?Solution
ATQ, Vowels = O, I, E, E Consonants = C, M, M, T, T Items = 1 (vowel block) + 5 = 6 (M twice, T twice) Arrangements = 6! / (2! × 2!) = 720 / 4 = 180 Arrangements of vowels = 4! / 2! = 24 / 2 = 12 Total words = 180 × 12 = 2160
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